nilpotent

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nil·po·tent

 (nĭl-pōt′nt, nĭl′pōt′nt)
n.
An algebraic quantity that when raised to a certain power equals zero.

[nil + Latin potēns, potent-, having power; see potent.]

nil·po′ten·cy n.

nilpotent

(nɪlˈpəʊtənt) maths
n
(Mathematics) a quantity that equals zero when raised to a particular power
adj
(Mathematics) equal to zero when raised to a particular power
ThesaurusAntonymsRelated WordsSynonymsLegend:
Adj.1.nilpotent - equal to zero when raised to a certain power
References in periodicals archive ?
By property [7.sup.0], [z.sub.kl] is a nilpotent element of K (x).
Note that [[delta].sub.0] nilpotent element of a ring is the zero element of the ring.
(ii) In NQR([Z.sub.4]), (2,2T, 21,2F) is a nilpotent element.
There exists a positive number [n.sub.2], depending only on [r.sub.0] and X, such that if [r.sub.2] [greater than or equal to] [n.sub.2] then [beta] ([[psi].sub.0]) contains a nilpotent element.
New and established researchers present 17 papers on such aspects of Lie algebras as gradings by groups on Cartan type Lie algebras, simple locally finite Lie algebras of diagonal type, constructing semi-simple sub-algebras of real semi-simple Lie algebras, regular derivations of truncated polynomial rings, some problems in the representation theory of simple modular Lie algebras, the conjugacy of nilpotent elements in characteristic p, problems of Lie properties of skew and symmetric elements of group rings, and open questions on modular Lie algebras.
A ring is called reduced if it has no nonzero nilpotent elements. By considering the right R-module M as an (S, R)-bimodule the reduced ring concept was considered for modules in [1].
whose image [[sigma].sub.g] in [g.sub.R] is a nilpotent cone in the absolute sense, i.e., the cone generated by finitely many mutually commuting nilpotent elements.
The structure of the set of nilpotent elements in Armendariz rings and the concept of nil-Armendariz as a generalization were introduced by Antoine (2008).