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- 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
- 12 bytes (1 word) - 15:35, 8 December 2008
- 162 bytes (23 words) - 02:15, 6 December 2008
- | pagename = Identity element | abc = Identity element2 KB (229 words) - 15:34, 8 December 2008
- 850 bytes (136 words) - 15:37, 8 December 2008
Page text matches
- * [[Identity element]], or neutral element, with respect to a binary operation, an element which591 bytes (78 words) - 12:52, 31 May 2009
- 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
- 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
- ...]] (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
- #REDIRECT [[Identity element]]30 bytes (3 words) - 16:01, 6 November 2008
- #REDIRECT [[Identity element]]30 bytes (3 words) - 14:42, 7 November 2008
- #REDIRECT [[Identity element]]30 bytes (3 words) - 14:43, 7 November 2008
- ...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
- * The zero (additive identity element) of a [[ring (mathematics)|ring]] is an absorbing element for the ring mult726 bytes (112 words) - 15:21, 21 December 2008
- ...r, off-diagonal, entries equal to zero. The identity matrix acts as the [[identity element]] for [[matrix multiplication]]. Its entries are those of the [[Kronecker1,020 bytes (136 words) - 10:39, 23 April 2009
- * 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
- An algebraic structure with an associative binary operation and an identity element.120 bytes (15 words) - 02:21, 9 November 2008
- {{r|Identity element}}514 bytes (67 words) - 21:47, 11 January 2010
- 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
- Examples include an [[identity element]] or an [[absorbing element]]. An important class of examples is formed by1,007 bytes (146 words) - 16:14, 13 December 2008
- {{r|Identity element}}965 bytes (124 words) - 17:23, 11 January 2010
- ...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
- {{r|Identity element}}969 bytes (124 words) - 18:42, 11 January 2010
- ...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
- | pagename = Identity element | abc = Identity element2 KB (229 words) - 15:34, 8 December 2008
- * [[Kernel of a homomorphism]], the elements mapped to the [[identity element]] by a [[homomorphism]]387 bytes (58 words) - 09:26, 30 September 2009
- * 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
- {{r|Identity element}}2 KB (247 words) - 06:00, 7 November 2010
- 2 KB (326 words) - 18:28, 17 July 2009
- ...al homomorphism''' between [[unital ring]]s (rings with a multiplicative [[identity element]]) must also satisfy2 KB (283 words) - 10:23, 6 January 2011
- ...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
- ...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
- * 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
- ...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
- Note that this means the [[identity element]] of the group is the [[identity map]] on <math>S</math>, which is the map8 KB (1,392 words) - 20:52, 25 June 2009
- {{rpl|Identity element}}5 KB (628 words) - 04:35, 22 November 2023
- ...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
- * ''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
- *I removed the existence of an identity element from the axioms. ...l to 0. The matrix with 1,1,0 in the diagonals and zeroes elsewhere is an identity element in the ideal although not in the larger ring.9 KB (1,551 words) - 10:52, 14 November 2007
- 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
- ...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 c5 KB (785 words) - 09:22, 30 July 2009
- ...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'' and18 KB (2,669 words) - 08:38, 17 April 2024
- ...the fractional ideal ''O''<sub>''K''</sub> = ''O''<sub>''K''</sub>.1 as [[identity element]]. The principal ideals, fractional ideals of the form ''O''<sub>''K''</su7 KB (1,077 words) - 17:18, 10 January 2009
- | existence of an [[identity element]]: || ''a'' + 0 = ''a'' || ''a'' &time10 KB (1,566 words) - 08:34, 2 March 2024
- ...ch element can be expressed as a product in only one way (up to use of the identity element, presumably), or whether it means that a given string can only represent on13 KB (2,191 words) - 21:34, 13 February 2009
- Thus, for instance, ''Gal(C/R)'' consists of two elements: the identity element27 KB (4,383 words) - 08:05, 11 October 2011