# idempotent

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## idempotent

(ˈaɪdəmˌpəʊtənt; ˈɪd-)
(Mathematics) maths (of a matrix, transformation, etc) not changed in value following multiplication by itself
[C20: from Latin idem same + potent1]

## i•dem•po•tent

(ˈaɪ dəmˈpoʊt nt, ˈɪd əm-)
1. (of a number or matrix) unchanged when multiplied by itself.
n.
2. an idempotent element.
[1870; idem + potent1]
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Adj. 1 idempotent - unchanged in value following multiplication by itself; "this matrix is idempotent"math, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangementunchanged - not made or become different; "the causes that produced them have remained unchanged"
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References in periodicals archive ?
Topics of the 27 papers include enveloping skewfields of the nilpotent positive part and Borel subsuperalgebra, good codes from metacyclic groups, generating characters on non-communtative Frobenius rings, U-rings generated by its idempotents, Panov's theorem for weak Hopf algebras, and a new approach to dualize retractable modules.
Thus they are idempotents in F(X, Y) such that [X.sub.a] = [X.sub.b][X.sub.a] = [X.sub.a][X.sub.b] = [X.sub.b]; it follows that a = b.
We can visualise the algebra [degrees]R[([GAMMA]).sub.v] as a quiver with the vertices given by the idempotents e(i) and the arrows labelled by generators [x.sub.1], ..., [x.sub.m], [[sigma].sub.0], ..., [[sigma].sub.m-1] and determined by the relationship between idempotents.
Moreover, the maximal subgroups of S are precisely the H-classes (see Section 2 below for definitions) of S which contain idempotents element.
Conversely, suppose that there exist idempotents x, [x.sub.1],...
The semisimple Hopf algebra kG* is commutative and the elements {[p.sub.g]} form a set of primitive idempotents for it.
From the biological point of view, the idempotents in the algebra [M.sub.4]([t.sub.F]) have their own usefulness.
We want to emphasize that the number of distinct primitive idempotents (four) and nilpotents (twelve), and there conjugates, coincides with the number of particle/antiparticle spices (bosons and fermions, respectively) of the standard model.
As A is semi-simple and commutative, A has also a basis of pairwise orthogonal idempotents [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where J denotes the all ones matrix.
Rearranging the terms in the decomposition of R in (7) based on the 3 types of primitive idempotents, we have
Then R<S [union] I> has non-trivial idempotents.

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