On the Lie structure of a prime associative superalgebra

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

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

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

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Cited by

  • Scopus Cited by: 0 (09-03-2023)
  • Web of Science Cited by: 0 (12-03-2023)

JCR (Journal Impact Factor)

  • Year 2014
  • Journal Impact Factor: 0.599
  • Journal Impact Factor without self cites: 0.475
  • Article influence score: 0.785
  • Best Quartile: Q3
  • Area: MATHEMATICS Quartile: Q3 Rank in area: 159/312 (Ranking edition: SCIE)

SCImago Journal Rank

  • Year 2014
  • SJR Journal Impact: 1.541
  • Best Quartile: Q1
  • Area: Algebra and Number Theory Quartile: Q1 Rank in area: 9/92

Scopus CiteScore

  • Year 2014
  • CiteScore of the Journal : 1.2
  • Area: Algebra and Number Theory Percentile: 53


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.