Results 231 to 240 of about 63,127 (261)

On Lie derivations of Lie ideals of prime algebras

Israel Journal of Mathematics, 2001
Let \(A\) be a prime associative algebra over a commutative ring with \(1\), let \(L\) be a noncentral Lie ideal of \(A\) with center \(Z(L)\), and let \(\overline L=L/Z(L)\) be the factor Lie algebra. Under some mild technical assumptions (namely, \(\text{char}(A)\neq 2\) and \(A\) does not satisfy \(S_{14}\), the standard polynomial identity of ...
Beidar, K. I., Chebotar, M. A.
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On ϕ-ideals and the structure of Lie algebras

Journal of Algebra and Its Applications, 2020
This paper aims to study the concept of [Formula: see text]-ideals of a finite-dimensional Lie algebra which is analogous to the concept of [Formula: see text]-ideal and [Formula: see text]-normal subgroup. We compile some basic properties of [Formula: see text]-ideals and consider the influence of this concept on the structure of a finite-dimensional
Goudarzi, Leila, Riyahi, Zahra
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Lie superhomomorphisms on Lie ideals in superalgebras

Israel Journal of Mathematics, 2013
In this paper the author investigates Lie superhomomorphisms from a Lie ideal of the skew elements of a superalgebra with superinvolution into a unital superalgebra. As a consequence a well-known result on Lie isomorphisms [\textit{K. I. Beidar} et al., Trans. Am. Math. Soc. 353, No.
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Derivations with Invertible Values on a Lie Ideal

Canadian Mathematical Bulletin, 1988
AbstractLet R be a ring which possesses a unit element, a Lie ideal U ⊄ Z, and a derivation d such that d(U) ≠ 0 and d(u) is 0 or invertible, for all u ∈ U. We prove that R must be either a division ring D or D2, the 2 X 2 matrices over a division ring unless d is not inner, R is not semiprime, and either 2R or 3R is 0.
J. BERGEN, CARINI, Luisa
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On ideals of free polynipotent lie algebras

Communications in Algebra, 1991
This paper investigates ideals in free polynilpotent Lie algebras. In §2 it is shown that if S is a non-zero finitely generated subalgebra that is an ideal in a free polynilpotent Lie algebra L, then S = L. In §3 it is proved that if L is a free polynilpotent Lie algebra and S is a nonabelian free polynilpotent ideal in L, then S is a term of the ...
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On Lie Ideals and Automorphisms in Prime Rings

Mathematical Notes, 2020
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Lie ideals and nil derivations

1985
Let R be a 2-torsion free ring, d a derivation of R, and U a Lie ideal of R. The authors obtain extensions to Lie ideals of some results in the literature for ideals. Specifically, by assuming that \(d(x)^{n(x)}=0\) for each \(x\in U\), they prove that \(d(U)=0\) when either: R is a semi- simple ring; R is a prime ring containing no nonzero nil right ...
CARINI, Luisa, A. GIAMBRUNO
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Densely embedded ideals of lie algebras

Siberian Mathematical Journal, 1974
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Centralizers and Lie ideals

1987
The author proves a version of I. N. Herstein's hypercenter theorem [\textit{I. N. Herstein}, J. Algebra 36, 151-157 (1975; Zbl 0313.16036)] for Lie ideals in prime rings. For any subset S in a ring R let the hypercenter of S be defined as \(H(S)=\{x\in R|\) for each \(s\in S\) there is \(n=n(x,s)>1\) so that \(xs^ n=s^ nx\}\).
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Notes on generalized Lie ideals

1999
Summary: \textit{J.~Bergen, I.~N.~Herstein} and \textit{J.~W.~Kerr} [J. Algebra 71, 259-267 (1981; Zbl 0463.16023)] have proved: Let \(R\) be a prime ring of characteristic \(\neq 2\). If \(U\) is a noncentral Lie ideal of \(R\), then there exists an ideal \(M\) of \(R\) such that \([M,R]\subseteq U\) but \([M,R]\not\subseteq Z\).
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