Results 231 to 240 of about 3,769 (264)

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
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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Lie Ideals and Central Identities With Derivation

Canadian Journal of Mathematics, 1992
AbstractIn this paper we consider various degree two central polynomials with derivation, holding for Lie ideals in prime rings. The results give substantial generalizations of the existing ones on central and semi-centralizing derivations, and show essentially that there are no central identities of the form p(x,y) = c1xyD + C2XDy + c3yxD + C4yDx ...
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