On the Lie structure of a prime associative superalgebra

  1. Laliena, J. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Journal:
Journal of Algebra

ISSN: 0021-8693

Year of publication: 2014

Volume: 404

Pages: 18-30

Type: Article

DOI: 10.1016/J.JALGEBRA.2014.02.001 SCOPUS: 2-s2.0-84893938022 WoS: WOS:000334565500002 arXiv: 1307.3243v1 GOOGLE SCHOLAR lock_openOpen access editor
Institutional repository: lock_openOpen access editor

Abstract

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 Φ with 1/2 ∈ Φ, if L is a Lie ideal of A and W is a subalgebra of A such that [. W, L] ⊆ W, then either L ⊆ Z or W ⊆ Z. Likewise, if V is a submodule of A and [. V, L] ⊆ V, then either V ⊆ Z or L ⊆ Z or there exists an ideal of A, M, such that 0 ≠ [. M, A] ⊆ V. This work extends to prime superalgebras some results of I.N. Herstein, C. Lanski and S. Montgomery on prime algebras. © 2014 Elsevier Inc.