In mathematics , an identityelement or neutral element is a special type of element of a Set mathematics ... identityelement is often shortened to identity as will be done in this article when there is no possibility ... magma . Then an element e of S is called a left identity if e a a for all a in S , and a right identity if a e a for all a in S . If e is both a left identity and a right identity, then it is called a two sided identity , or simply an identity . An identity with respect to addition is called an additive identity often denoted as 0 and an identity with respect to multiplication is called a multiplicative identity often denoted as 1 . The distinction ... f would have to be equal to both e and f . It is also quite possible for S , to have no identityelement ... of an identityelement is related to the fact that the Direction geometry direction of any nonzero ... Binary operations Identityelement Category One NOTOC ar bg ... neutro ru simple Identityelement sk Neutr lny prvok sl Nevtralni element ... identity is often called the unit in the latter context, where, unfortunately, a unit ring theory unit is also sometimes used to mean an element with a multiplicative inverse. Examples class wikitable style margin 1em auto 1em auto set operation identity real number s addition 0 number 0 real number s multiplication 1 number 1 real number s a sup b sup exponentiation 1 right identity ... I sub n sub identity matrix matrix with 1 on diagonal br and 0 elsewhere all function mathematics functions from a set M to itself function composition identity function all function mathematics ... identity br and no two sided identity Properties As the last example shows, it is possible for S , to have several left identities. In fact, every element can be a left identity. Similarly, there can be several right identities. But if there is both a right identity and a left identity ... more details
wiktionary Element may refer to Chemistry, electronics, or the geosciences Chemical element , a building block in chemistry Electrical element , an abstract part of a circuit Heating element , a device that generates heat by electrical resistance Weather , sometimes referred to as the elements Computing Adobe Photoshop Elements , a bitmap graphics program Adobe Premiere Elements , a video editing computer program Array data structure elements Data element , a unit of data HTML element , a standard part of a HTML document Law Element criminal law , a basic set of common law principles regarding criminal liability Mathematics Element mathematics , one of the constituents of a set Euclid s Elements Euclid s Elements , a mathematical treatise on geometry and number theory Music Element production team , a Norwegian production and songwriting team Elements Atheist album Elements Atheist album Elements band , 1980s 90s American jazz ensemble Elements Roger Glover album Elements Roger Glover album Elements Steve Howe album Elements Steve Howe album Elements, Pt. 1 , an album by Stratovarius Elements, Pt. 2 , an album by Stratovarius The Elements album The Elements album , a 2007 album by Second ... element s, part of a traditional belief system Five elements Japanese philosophy , the basis ... , the basis of the universe according to Chinese Taoism Other Element by Westin, a brand of Starwood Hotels and Resorts Worldwide Element by Westin Starwood Hotels and Resorts Worldwide Element Skateboards , a skateboard manufacturer Elements, Hong Kong , a shopping mall in Hong Kong Honda Element ... Element cs Element cy Elfen de Element et Element es Elemento eo Elemento eu Elementu fa fr l ment fur Element ga D il gv Elmint gl Elemento ko io Elemento id Unsur disambiguasi ia Elemento disambiguation ... Unsur nl Element ja pap Elemento pl Element pt Elementos ro Element ru simple Element sk Element sl Element fi Elementti sv Element tl Elemento tt tg uk vi Nguy n ... more details
Infobox rfam Name S element image RF00490.jpg width caption Predicted secondary structure and sequence conservation of S element Symbol S element AltSymbols Rfam RF00490 miRBase miRBase family RNA type Cis regulatory element Cis reg Tax domain Bacteria GO SO SO 0000233 CAS number EntrezGene HGNCid OMIM PDB RefSeq Chromosome Arm Band LocusSupplementaryData The S element is an cis regulatory element RNA element found in p42d and related plasmid s. The S element has multiple functions and is believed to act as a negative regulator of repC Transcription genetics transcription , and be required for efficient replication and act as a translation al enhancer of repC. ref cite journal last Venkova Canova first T coauthors Soberon NE, Ramirez Romero MA, Cevallos MA year 2004 title Two discrete elements are required for the replication of a repABC plasmid an antisense RNA and a stem loop structure journal Mol Microbiol volume 54 pages 1431&ndash 1444 pmid 15554980 doi 10.1111 j.1365 2958.2004.04366.x issue 5 ref See also ctRNA References reflist 1 External links Rfam id RF00490 name S element Category Cis regulatory RNA elements molecular cell biology stub ... more details
identity , belief in membership of a nation Mathematics Identityelement , a special element in a set or structure with respect to an operator Identity function , a function that does not alter its argument Identity mathematics , an equality that holds regardless of the values of its variables Identity matrix , a square matrix with ones on the main diagonal , zeros elsewhere Business Accounting identity , calculation or measurement that must be true regardless of the value of its variables Corporate identity , persona of a corporation by way of branding or use of trademarks Computer science Digital identity , representation of a set of claims made by one digital subject about itself or another ...wiktionary tocright Identity may refer to Philosophical topics Identity philosophy , also called sameness, is whatever makes an entity definable and recognizable Law of identity , principle of logic stating that an object is the same as itself Personal identity philosophy , refers to the numerical identity continuity of existence of persons through time Specifications of persons Identity change Identity document Identity theft , the deliberate appropriation of someone else s identity without that person ... Gender identity , also known as core gender identity, the gender s or lack thereof, that a person self identifies Identity formation , the process of the development of the distinct personality of an individual Identity social science , umbrella term used to describe individuality, personal identity, social identity, and cultural identity in psychology, sociology, and philosophy Persona , a social role or a character played by an actor with oneself Sexual orientation identity , describes how persons identify their own sexuality Group expression and affiliation Christian Identity , a Christian religious movement Cultural identity , person s self affiliation or categorization by others as a member of a cultural group Identity politics , refers to political arguments that focus ... more details
Identityelement Null semigroup Notes reflist 2 References cite book last Howie first John M. title ...In mathematics , an absorbing element is a special type of element of a Set mathematics set with respect to a binary operation on that set. The result of combining an absorbing element with any element of the set is the absorbing element itself. In semigroup theory, the absorbing element is called a Semigroup Identity and zero zero element ref J.M. Howie, p. 2 3 ref ref name kkm M. Kilp, U. Knauer, A.V. Mikhalev p. 14 15 ref because there is no risk of confusion with zero element other notions of zero. In this article the two notions are synonymous. Definition Formally, let S , be a set S with a binary operation on it known as a magma algebra magma . A zero element is an element z such that for all s in S , z s s z z . A refinement ref name kkm are the notions of left zero , where one requires only that z s z , and right zero , where s z z . Absorbing elements are particularly interesting for semigroup s, especially the multiplicative semigroup of a semiring . In the case of a semiring with 0, the definition of an absorbing element is sometimes relaxed so that it is not required to absorb 0 otherwise, 0 would be the only absorbing element. ref J.S. Golan p. 67 ref Properties If a magma has both a left zero math z math and a right zero math z math , then it has a zero, since math z z times z z math . If a magma has a zero element, then the zero element is Uniqueness quantification unique . Examples The set of binary relations over a set X , together with the composition of relations forms a monoid with zero, where the zero element is the empty relation empty set . The closed ... element is 0. More examples class wikitable style margin 1em auto 1em auto set operation absorber ... element at PlanetMath Category Semigroup theory Category Binary operations Absorbing element NOTOC de Absorbierendes Element es Elemento absorbente fr l ment absorbant nl Absorberend element ja ... more details
In mathematics , a zero element is one of several generalizations of 0 number the number zero to other algebraic structure s. These alternate meanings may or may not reduce to the same thing, depending on the context. Additive identities An additive identity is the identityelement in an additive group . It generalises the property nowrap 0 x x . Examples include The null vector under vector addition The zero function or zero map , defined by nowrap z x 0, under function addition, nowrap f g x f x g x , since nowrap z f f . The empty set under Union set theory set union An empty sum or empty coproduct An Initial and terminal objects initial object in a category mathematics category an empty coproduct, and so an identity under coproduct s Absorbing elements An absorbing element in a multiplicative semigroup or semiring generalises the property nowrap 0 x 0. Examples include The empty set , which is an absorbing element under Cartesian product of sets, since S The zero function or zero map , defined by nowrap z x 0, under function multiplication, nowrap f g x f x g x , since nowrap z f z . Many absorbing elements are also additive identities, including the empty set and the zero function. Another important example is the distinguished element 0 in a field mathematics field or ring mathematics ring , which is both the additive identity and the multiplicative absorbing element, and whose ... is both an Initial and terminal objects initial and terminal object and so an identity under ... only the identity is a zero object in categories where morphisms must map identities to identities. Specific examples include The trivial group , containing only the identity a zero object in the category of groups The zero module , containing only the identity a zero object in the category of module ... is a generalised absorbing element under function composition any morphism composed with a zero morphism ... element in a partially ordered set or Lattice order lattice may sometimes be called a zero element ... more details
, p. 180 ref Intuitively, quasiregularity captures what it means for an element of a ring to be bad that is, have undesirable properties. ref Isaacs, p. 179 ref Although a bad element is necessarily ... of noncommutative ring theory. Definition Let R be a ring with multiplicative identity unity and let r be an element of R . Then r is said to be quasiregular , if 1 r is a Unit ring theory unit in R ... name Isaacs, p. 180 An element x of a non unital ring is said to be right quasiregular if there is y such that math xy x y 0 math . ref Kaplansky, p. 85 ref The notion of a left quasiregular element is defined in an analogous manner. The element y is sometimes referred to as a right quasi inverse of x . ref Polcino & Sehgal 2002 , Google books quote id 7m9P9hM4pCQC page 298 text this element is called ... math cdot math is associative. Therefore, if an element possesses both a left and right quasi inverse, they are equal. ref Since 0 is the multiplicative identity, if math x cdot y 0 y cdot x math , then math ... a multiplicative identity. ref Examples If R is a ring, then the additive identity of R is always ... quasiregular. ref Kaplansky, p. 108 ref If R is a ring, every nilpotent element of R is quasiregular ... the ring of formal power series in n intederminants over R , an element of S is quasiregular if and only its constant term is quasiregular as an element of R . Properties Every element of the Jacobson ..., maximal with respect to the property that every element is right quasiregular. ref Isaacs, Theorem 13.4 b , p. 180 ref ref Isaacs, Corollary 13.7, p. 181 ref However, a right quasiregular element .... If an element of a ring is nilpotent and Center of a ring central , then it is a member of the ring ... right ideal generated by that element consists of quasiregular in fact, nilpotent elements only. If an element, r , of a ring is Idempotent element idempotent , it cannot be a member of the ring ... Nilradical Unit ring theory Nilpotent element Center of a ring Idempotent element Category Ring ... more details
Element name may refer to A data element name in a database A name of a chemical element . See also Systematic element name , List of elements by name , and List of chemical element name etymologies . disambig ... more details
magma . If math e math is an identityelement of math S, math i.e., S is an unital magma and math ...In abstract algebra , the idea of an inverse element generalises the concept of a additive inverse negation ... . The intuition is of an element that can undo the effect of combination with another given element. While the precise definition of an inverse element varies depending on the algebraic structure ... a right inverse of math a math . If an element math x math is both a left inverse and a right inverse ... math . An element with a two sided inverse in math S math is called invertible in math S math . An element with an inverse element only on one side is left invertible , resp. right invertible . If all ... left identities or several right identities, it is possible for an element to have several left inverses or several right inverses but note that their definition above uses a two sided identity math ... math is associative then if an element has both a left inverse and a right inverse, they are equal. In other words, in a monoid every element has at most one inverse as defined in this section . In a monoid ... of units of math S math , and denoted by math U S math or H sub 1 sub . A left invertible element ... relative to the notion of identity. It s also possible, albeit less obvious, to generalize the notion of an inverse by dropping the identityelement but keeping associativity, i.e. in a semigroup . In a semigroup math S math an element x is called von Neumann regular if there exists some element z in S such that xzx x z is sometimes called a pseudoinverse . An element y is called simply an inverse of x if xyx x and y yxy . Every regular element has at least one inverse if x xzx then it is easy ... identity on x , while f acts a right identity, and the left right roles are reversed for y . This simple ... semigroup is a left identity for R sub e sub and right identity for L sub e sub . ref Howie, prop ... produces a local left identity, and respectively, a local right identity. In a monoid, the notion ... more details
unreferenced date April 2011 In chemistry , a free element is a chemical element that is uncombined with other elements. Category Chemistry chem stub ... more details
About the Banach algebra concept Approximation to the identity disambiguation Approximation to the identity In functional analysis and ring theory, an approximate identity is a net in a Banach algebra or ring possibly without an identity that acts as a substitute for an identityelement. More precisely, a right approximate identity in a Banach algebra , A , is a net mathematics net or a sequence math ,e lambda lambda in Lambda , math such that for every element, a , of A , the net or sequence math ,ae lambda lambda in Lambda , math has limit a . Similarly, a left approximate identity is a net math ,e lambda lambda in Lambda , math such that for every element, a , of A , the net or sequence math ,e lambda a lambda in Lambda , math has limit a . An approximate identity is a right approximate identity which is also a left approximate identity. For C algebra s, a right or left approximate identity is the same as an approximate identity. Every C algebra has an approximate identity of positive element positive elements of norm &le 1 indeed, the net of all positive elements of norm &le 1 in A with its natural order always suffices. This is called the canonical approximate identity of a C algebra. Approximate identities of C algebras are not unique. For example, for compact operators acting on a Hilbert space, the net consisting of finite rank projections would be another approximate identity. An approximate identity in a convolution algebra plays the same role as a sequence of function approximations to the Dirac delta function which is the identityelement for convolution . For example the Fej r kernel s of Fourier series theory give rise to an approximate identity. Ring theory In ring theory an approximate identity is defined in a similar way, except that the ring is given the discrete topology so that a ae sub sub for some . A module over a ring with approximate identity is called non degenerate if for every m in the module there is some with m me sub sub . See also ... more details
In mathematics, the term primitive element can mean Primitive root modulo n Primitive root modulo n , in number theory Primitive element field theory , an element that generates a given field extension Primitive element finite field , an element that generates the multiplicative group of a finite field in a Hopf algebra , an element X on which the comultiplication has the value X X 1 1 X in a free group , an element of a free generating set See also primitive root disambiguation mathdab ... more details
Regular element may refer to In ring theory , a nonzero element of a ring that is neither a left nor a right zero divisor A regular element of a Lie algebra or Lie group. mathdab ... more details
Element 0 may refer to Neutronium , sometimes referred to as an element with atomic number 0 Element Zero, or eezo, the primary power source used in the video game series Mass Effect series Mass Effect . disambig ... more details
A transfermium element is a chemical element with atomic number greater than 100, that of Fermium . The transfermium elements have a number of common characteristics they Synthetic element do not occur naturally they are difficult to produce in a laboratory they have very short half lives and are radioactive . See also Transuranium element Transactinide element Category Chemical elements chem stub ... more details
Element 6 can refer to Carbon element with atomic number 6 Element Six formerly De Beers Industrial Diamond a company specialised in providing superhard material solutions such as synthetic diamond, cubic boron nitride for industrial applications disambig ... more details
Response elements are short sequences of DNA within a gene promoter region that are able to bind a specific transcription factor and regulate Transcription genetics transcription of gene s. Examples Examples of response elements include Hormone response element cAMP response element External links MeshName response element Category DNA Biochemistry stub Transcription ... more details
A Virasoro element is a distinguished element of one of several related mathematical strutures Virasoro algebra Super Virasoro algebra Vertex operator algebra Vertex operator superalgebra mathdab ... more details
Fifth Element may refer to 5th Element , the 1999 album by reggae and dancehall artist Bounty Killer The 5th Element Tynisha Keli album The 5th Element Tynisha Keli album Aether classical element , the mythical fifth classical element Aether classical element Quintessence , another term for the fifth element Boron , the modern element with atomic number 5 on the periodic table The Fifth Element , a 1997 movie starring Bruce Willis The Fifth Element video game The Fifth Element video game , a 1998 video game based on the movie The Fifth Element store , a hip hop record store in Uptown, Minneapolis The Fifth Sacred Thing , which has apparently been referred to also as The Fifth Element , is a novel by Starhawk The apparently erroneous reference is in Sch npflug, Karin, Feminism, Economics and Utopia Time Travelling Through Paradigms Oxon London Routledge Routledge Frontiers of Political Economy ser., no. 99 , hbk. 2008 ISBN13 978 0 415 41784 6 , p. 22 and perhaps see chap. 7 author economist, Austrian Ministry of Finance, & lecturer, Univ. of Vienna, Austria, per id. , p. i author Sch npflug named Starhawk s work as The Fifth Element in original but perhaps intended The Fifth Sacred Thing , per http www.worldcat.org search?q ti 3AThe Fifth au 3AStarhawk&qt advanced&dblist 638 as accessed Nov. 18, 2011, as no work titled The Fifth Element by Starhawk is known, per http www.worldcat.org search?q ti 3AThe Fifth Element au 3AStarhawk&qt results page as accessed Nov. 18, 2011 . disambig ru zh ... more details
Unreferenced stub auto yes date December 2009 Orphan date December 2009 An octatomic element is a chemical element that, under standard conditions for temperature and pressure is stable, when in a configuration of eight atoms grouped together. The canonical example is sulfur , S sub 8 sub , but also octaoxygen is known. See also Diatomic element DEFAULTSORT Octatomic Element Category Molecules Chem stub ... more details
Surface element may refer to Volume form Surfel in 3D computer graphics Differential infinitesimal , an infinitesimal portion of a surface disamb ... more details
Unreferenced stub auto yes date December 2009 In an electric electrical network circuit , a linear element is an electrical element with a linear relationship between input electricity current and output voltage . Resistor s are the most common example of a linear element other examples include capacitor s, inductor s, and transformer s. Fundamentally nonlinear devices like transistors are often used to build approximately linear circuits. For example, an Operational amplifier op amp is designed to behave like a linear amplifier, as long as its input voltages remain within certain limits. See also Nonlinear element DEFAULTSORT Linear Element Category Electronics terms Electronics stub zh ... more details
unreferenced date May 2011 Orphan date May 2011 The beam element is a mathematical construct used to model beam type structures. The beam is a common structure used in engineering. The frame of a steel building , the frame of a vehicle street lights can all be described by beams. For these reasons the element is used frequently in finite element analysis . The typical beam element assumes all loading is discrete at the ends of the beam. In cases where there is intermediate loading, multiple elements are used. If the intermediate loading is distributed, a load lumping scheme needs to be applied to map the forces to the node. In these situations the beam element fails to give the analytical solution for beam deflection. Provided that a consistent load lumping scheme is applied the element will predict the correct internal forces and displacement at the nodes. Thus by including increasingly more beam elements to a problem, the solution will converge to the exact result. Category Mathematical modeling ... more details
Element 4 may refer to Beryllium with the atomic number 4 Elementfour , a music producing duo made up of Paul Oakenfold and Andy Gray disambig ... more details
Unreferenced date December 2009 A literary element or element inside literature is an element found in whole works of literature . Literary elements are not used by authors but instead, they exist inherently in forms of literature and are derived by the readers of a work in question. Theme literature Theme , characterization , conflict narrative conflict , Setting fiction setting , protagonist , antagonist , and point of view literature point of view are among the many literary elements that exist. They can be about the setting, plot, or even the characters. An example of this is foreshadowing. Some examples of this can include Motifs, Symbols, Conflicts, and Allusions. DEFAULTSORT Literary Element Category Literature ... more details
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