On the Lie structure of a prime associative superalgebra

JOURNAL OF ALGEBRA

卷:404

Article

Laliena, Jesus

关键词: Associative superalgebras;    Prime superalgebras;    Lie structure;   

DOI  :  10.1016/j.jalgebra.2014.02.001

来源: Elsevier

【 摘 要 】

In this paper some results on the Lie structure of prime superalgebras are discussed. We prove that, with the exception of some special cases, for a prime superalgebra A over a ring of scalars phi with 1/2 is an element of phi, if L is a Lie ideal of A and W is a subalgebra of A such that [W, L] subset of W, then either L subset of Z or W subset of Z. Likewise, if V is a submodule of A and [V, L] C V, then either V C Z or L C Z or there exists an ideal of A, M, such that 0 not equal [M, A] subset of V. This work extends to prime superalgebras some results of I.N. Herstein, C. Lanski and S. Montgomery on prime algebras. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free