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Izv. RAN. Ser. Mat., 2017, Volume 81, Issue 1, Pages 93–100 (Mi izv8387)  

This article is cited in 1 scientific paper (total in 1 paper)

On special Lie algebras having a faithful module with Krull dimension

O. A. Pikhtilkova, S. A. Pikhtilkov

Orenburg State University, Faculty of Mathematics

Abstract: For special Lie algebras we prove an analogue of Markov's theorem on $\mathrm{PI}$-algebras having a faithful module with Krull dimension: the solubility of the prime radical. We give an example of a semiprime Lie algebra that has a faithful module with Krull dimension but cannot be represented as a subdirect product of finitely many prime Lie algebras. We prove a criterion for a semiprime Lie algebra to be representable as such a subdirect product.

Keywords: special Lie algebra, prime radical of a Lie algebra, faithful module with Krull dimension.

DOI: https://doi.org/10.4213/im8387

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English version:
Izvestiya: Mathematics, 2017, 81:1, 91–98

Bibliographic databases:

UDC: 512.554.34
MSC: 17B05, 17B30, 17B60
Received: 09.04.2015
Revised: 16.09.2015

Citation: O. A. Pikhtilkova, S. A. Pikhtilkov, “On special Lie algebras having a faithful module with Krull dimension”, Izv. RAN. Ser. Mat., 81:1 (2017), 93–100; Izv. Math., 81:1 (2017), 91–98

Citation in format AMSBIB
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  • https://doi.org/10.4213/im8387
  • http://mi.mathnet.ru/eng/izv/v81/i1/p93

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. N. Blagovisnaya, O. A. Pikhtilkova, S. A. Pikhtilkov, “On the M.V. Zaicev problem for a Noetherian special Lie algebras”, Russian Math. (Iz. VUZ), 61:5 (2017), 21–25  mathnet  crossref  isi
  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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