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

    GRID grid.119021.a

Journal:
Journal of Algebra

ISSN: 0021-8693

Year of publication: 2014

Volume: 404

Pages: 18-30

Type: Article

Export: RIS
DOI: 10.1016/j.jalgebra.2014.02.001 SCOPUS: 2-s2.0-84893938022 WoS: 000334565500002 arXiv: 1307.3243v1 GOOGLE SCHOLAR lock_openOpen access editor
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Metrics

Cited by

  • Scopus Cited by: 0 (12-06-2021)

Journal Citation Reports

  • Year 2014
  • Journal Impact Factor: 0.599
  • 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

CiteScore

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

Summary

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.