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• Identity element
  In [[algebra]], an '''identity element''' or '''neutral element''' with respect to a [[binary operation]] is an el holds for all ''x'' in ''X''. An identity element, if it exists, is unique.
  927 bytes (140 words) - 15:33, 8 December 2008
• Identity element/Definition
  162 bytes (23 words) - 02:15, 6 December 2008
• Identity element/Related Articles
  850 bytes (136 words) - 15:37, 8 December 2008

Page text matches

• Identity (mathematics)
  * [[Identity element]], or neutral element, with respect to a binary operation, an element which
  591 bytes (78 words) - 12:52, 31 May 2009
• Identity element
  In [[algebra]], an '''identity element''' or '''neutral element''' with respect to a [[binary operation]] is an el holds for all ''x'' in ''X''. An identity element, if it exists, is unique.
  927 bytes (140 words) - 15:33, 8 December 2008
• Group (mathematics)/Definition
  Set with a binary associative operation such that the operation admits an identity element and each element of the set has an inverse element for the operation.
  197 bytes (30 words) - 08:22, 4 September 2009
• Order (group theory)
  ...]] (if one exists) such that raising the element to that power gives the [[identity element]] of the group. If there is no such number, the element is said to be of '
  857 bytes (146 words) - 13:24, 1 February 2009
• Neutral element
  #REDIRECT [[Identity element]]
  30 bytes (3 words) - 16:01, 6 November 2008
• Additive identity
  #REDIRECT [[Identity element]]
  30 bytes (3 words) - 14:42, 7 November 2008
• Multiplicative identity
  #REDIRECT [[Identity element]]
  30 bytes (3 words) - 14:43, 7 November 2008
• Identity function
  ...n [[inverse function]]). It is a [[permutation]] of the set, and is the [[identity element]] of the [[symmetric group]] on ''X''.
  425 bytes (64 words) - 15:38, 7 February 2009
• Absorbing element
  * The zero (additive identity element) of a [[ring (mathematics)|ring]] is an absorbing element for the ring mult
  726 bytes (112 words) - 15:21, 21 December 2008
• Identity matrix
  ...r, off-diagonal, entries equal to zero. The identity matrix acts as the [[identity element]] for [[matrix multiplication]]. Its entries are those of the [[Kronecker
  1,020 bytes (136 words) - 10:39, 23 April 2009
• Monoid
  * There is an [[identity element]] <math>I \in M</math> such that ...have at most one inverse (note that <math>x = y^{-1}</math> as well). The identity element is self-inverse and the product of invertible elements is invertible,
  3 KB (526 words) - 11:02, 23 December 2008
• Monoid/Definition
  An algebraic structure with an associative binary operation and an identity element.
  120 bytes (15 words) - 02:21, 9 November 2008
• Zero matrix/Related Articles
  {{r|Identity element}}
  514 bytes (67 words) - 21:47, 11 January 2010
• Identity matrix/Definition
  A square matrix with ones on the main diagonal and zeroes elsewhere: the identity element for matrix multiplication.
  152 bytes (21 words) - 13:19, 5 December 2008
• Idempotent element
  Examples include an [[identity element]] or an [[absorbing element]]. An important class of examples is formed by
  1,007 bytes (146 words) - 16:14, 13 December 2008
• Identity matrix/Related Articles
  {{r|Identity element}}
  965 bytes (124 words) - 17:23, 11 January 2010
• Group homomorphism
  ...a homomorphism''' is the set of all elements of the domain that map to the identity element of the codomain. This subset is a [[normal subgroup]], and every normal su ...ve]] homomorphism (or, equivalently, one whose kernel consists only of the identity element).
  1 KB (210 words) - 01:00, 11 February 2009
• Multiplication/Related Articles
  {{r|Identity element}}
  969 bytes (124 words) - 18:42, 11 January 2010
• Pointed set
  ...cs)|group]] or [[vector space]] have a distinguished element, such as an [[identity element]], and [[morphism]]s of the structures respect those elements.
  1 KB (168 words) - 12:06, 22 November 2008
• Kernel (mathematics)
  * [[Kernel of a homomorphism]], the elements mapped to the [[identity element]] by a [[homomorphism]]
  387 bytes (58 words) - 09:26, 30 September 2009
• Subgroup
  * The [[identity element]] of ''G'' is an element of ''S''; The group itself and the set consisting of the identity element are always subgroups.
  4 KB (631 words) - 07:56, 15 November 2008
• Algebra/Related Articles
  {{r|Identity element}}
  2 KB (247 words) - 06:00, 7 November 2010
• Zero (mathematics)
  2 KB (326 words) - 18:28, 17 July 2009
• Ring homomorphism
  ...al homomorphism''' between [[unital ring]]s (rings with a multiplicative [[identity element]]) must also satisfy
  2 KB (283 words) - 10:23, 6 January 2011
• Free group
  ...the [[binary operation]] of concatenation (juxtaposition) of words. The [[identity element]] for this operation is the empty string. (So far we have described the [[
  2 KB (436 words) - 02:56, 15 November 2008
• Ring (mathematics)
  ...which multiplication is commutative and every element except the additive identity element (0) has a multiplicative inverse (reciprocal) is called a [[field]]: for ex ...bly [[Nicholas Bourbaki|Bourbaki]], demand that their rings should have an identity element, and call rings without an identity ''pseudorings''.
  10 KB (1,667 words) - 13:47, 5 June 2011
• Semigroup
  * Every [[monoid]] is a semigroup, by "forgetting" the identity element. * Every [[group (mathematics)|group]] is a semigroup, by "forgetting" the identity element and inverse operation.
  3 KB (405 words) - 16:21, 13 November 2008
• Commutator
  ...ommute if and only if the commutator [''x'',''y''] is equal to the group [[identity element|identity]]. The '''commutator subgroup''' or '''derived group''' of ''G''
  1 KB (217 words) - 15:16, 11 December 2008
• Symmetric group
  Note that this means the [[identity element]] of the group is the [[identity map]] on <math>S</math>, which is the map
  8 KB (1,392 words) - 20:52, 25 June 2009
• Field (mathematics)
  ...er binary operation ''*'' on F such that F\{0} is a commutative group with identity element 1. [[Distributivity]] of ''*'' over ''+'' holds: that is, for any <math>a,
  3 KB (496 words) - 22:16, 7 February 2010
• Group theory
  * ''The group has an [[identity element]]:'' There is an element <math>e</math>, such that <math>x \cdot e = x</mat ...\cdot y = e</math> and <math>y \cdot x = e</math>. (<math>e</math> is the identity element)
  15 KB (2,535 words) - 20:29, 14 February 2010
• Group (mathematics)
  The neutral element of a group is often called the [[identity element]] if the operation is written in [[multiplicative group|multiplicative]] no * 0 is an integer and for any integer ''a'', 0 + ''a'' = ''a'' + 0 = ''a''. (Identity element)
  19 KB (3,074 words) - 11:11, 13 February 2009
• Normal subgroup
  ...homomorphism <math>\phi: G \to K</math> such that the inverse image of the identity element of ''K'' is ''H''. and the coset <math>N = N1</math> as [[identity element]]. It is easy to check that these define a group structure on the set of c
  5 KB (785 words) - 09:22, 30 July 2009
• Algebra
  ...However, if we take the positive natural numbers and addition, there is no identity element. * An identity element ''e'' exists, such that for every member ''a'' of ''S'', ''e'' * ''a'' and
  18 KB (2,669 words) - 08:38, 17 April 2024
• Algebraic number field
  ...the fractional ideal ''O''_''K'' = ''O''_''K''.1 as [[identity element]]. The principal ideals, fractional ideals of the form ''O''<sub>''K''</su
  7 KB (1,077 words) - 17:18, 10 January 2009
• Integer
  | existence of an [[identity element]]: || ''a''&nbsp;+&nbsp;0&nbsp;&nbsp;=&nbsp;&nbsp;''a'' || ''a''&nbsp;&time
  10 KB (1,566 words) - 08:34, 2 March 2024
• Number theory
  Thus, for instance, ''Gal(C/R)'' consists of two elements: the identity element
  27 KB (4,383 words) - 08:05, 11 October 2011