nilradical

nilradical

[‚nil′rad·ə·kəl]
(mathematics)
For an ideal, I, in a ring, R, the set of all elements, a, in R for which an is a member of I for some positive integer n. Also known as radical.
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Let [square root of 0] be the nilradical of [H.sup.*](BA; Z/3) and [H.sup.*](B[mu]; Z/3), so that we have the induced homomorphism
As in the previous section, we denote the nilradical by [square root of 0] and we denote the inclusion map of [mu] to A by [[iota].sub.1] : [mu] [right arrow] A.
Among the topics are characterization conditions and the numerical index, the generalized localization of a Fourier inversion for distributions, algebras with genetic realization and corresponding evolutionary population dynamics, complex powers of the Schr|dinger operator with singular potential, a description of solvable Leibniz algebras with a four-dimensional nilradical, and an invitation to research new mathematics from biology: evolution algebras.
Using (H3), we can show that u is the nilradical of the parabolic subalgebra [p.sub.I].
It follows from hypothesis (H3) in the introduction that u is the nilradical of the parabolic subalgebra [p.sub.I].
B-stable ideals in the nilradical of a Borel subalgebra.
The set of all nilpotent elements of R is called nilradical of R and it is denoted by Nil (R).
Here, [sigma] :[Sym.sup.k](g(-1)) [right arrow] U([??]) is the symmetrization operator, R is the infinitesimal right translation, and D[([L.sub.S]).sup.[bar.n]] is the space of [bar.n]-invariant differential operators for [L.sub.s] with [bar.n] the opposite nilradical of n.
Sommers, B-stable ideals in the nilradical of a Borel subalgebra, Canad.