On Lie derivations of Lie ideals of prime algebras期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On Lie derivations of Lie ideals of prime algebras

Authors:	K. I. Beidar M. A. Chebotar

Affiliation:	(1) Department of Mathematics, National Cheng-Kung University, Tainan, Taiwan;(2) Department of Mechanics and Mathematics, Moscow State University, Moscow, Russia

Abstract:	LetF be a commutative ring with 1, letA, be a primeF-algebra with Martindale extended centroidC and with central closureA _c and letR be a noncentral Lie ideal of the algebraA generatingA. Further, letZ(R) be the center ofR, let be the factor Lie algebra and let δ: be a Lie derivation. Suppose that char(A) ≠ 2 andA does not satisfySt ₁₄, the standard identity of degree 14. We show thatR ΩC =Z(R) and there exists a derivation of algebrasD:A →A _c such that $x^D + {mathcal{C}} = left( {x + {mathcal{C}}} right)^delta in left( {mathcal{R} + {mathcal{C}}} right)/{mathcal{C}} = bar {mathcal{R}}$ for allx∈R. Our result solves an old problem of Herstein.

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