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Inner Ideals of Simple Locally Finite Lie Algebras
Journal of Algebra, 2013 Inner ideals of simple locally finite dimensional Lie algebras over an algebraically closed field of characteristic 0 are described. In particular, it is shown that a simple locally finite dimensional Lie algebra has a non-zero proper inner ideal if and ...
Jamie Robert Derek Rowley (7675763)
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On ideals of free polynipotent lie algebras
Communications in Algebra, 1991This 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, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Densely embedded ideals of lie algebras
Siberian Mathematical Journal, 1974zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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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Lie ideals and nil derivations
1985Let 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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Notes on generalized Lie ideals
1999Summary: \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, 1992AbstractIn 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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Representations Subduced on an Ideal of a Lie Algebra
Canadian Journal of Mathematics, 1962This paper considers the properties of the representation of a Lie algebra when restricted to an ideal, the subduced* representation of the ideal. This point of view leads to new forms for irreducible representations of Lie algebras, once the concept of matrices of invariance is developed.
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2021
SUMMARY In the first chapter, we give some basis definations and properties. In the 2nd chapter, it is given some important properties about the Lie and Jordan ideals. Also in this chapter, it is seen that a given ring is commutative under some conditions In the 3nd chapter, we generalized some consequences on Lie and Jordan frames which are obtained ...
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SUMMARY In the first chapter, we give some basis definations and properties. In the 2nd chapter, it is given some important properties about the Lie and Jordan ideals. Also in this chapter, it is seen that a given ring is commutative under some conditions In the 3nd chapter, we generalized some consequences on Lie and Jordan frames which are obtained ...
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