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Algebra i logika, 2020, Volume 59, Number 5, Pages 517–528
DOI: https://doi.org/10.33048/alglog.2020.59.501 (Mi al2631) 		 
Associative algebras with a distributive lattice of subalgebras

A. G. Gein

Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
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DOI: https://doi.org/10.33048/alglog.2020.59.501
Abstract: We give a full description of associative algebras over an arbitrary field, whose subalgebra lattice is distributive. All such algebras are commutative, their nil-radical is at most two-dimensional, and the factor algebra with respect to the nil-radical is an algebraic extension of the base field.
Keywords: lattice of subalgebras, distributive lattice, lattice of subextensions of field.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 02.A03.21.0006
Supported through the Competitiveness Project (Agreement No. 02.A03.21.0006 of 27.08.2013 between the Ministry of Education and Science of the Russian Federation and the Ural Federal University).
Received: 18.01.2020
Revised: 27.11.2020
English version:
Algebra and Logic, 2020, Volume 59, Issue 5, Pages 349–356
DOI: https://doi.org/10.1007/s10469-020-09608-6
Bibliographic databases:
Document Type: Article
UDC: 512.552.3
Language: Russian
Citation: A. G. Gein, “Associative algebras with a distributive lattice of subalgebras”, Algebra Logika, 59:5 (2020), 517–528; Algebra and Logic, 59:5 (2020), 349–356
Citation in format AMSBIB
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\by A.~G.~Gein
\paper Associative algebras with a distributive lattice of subalgebras
\jour Algebra Logika
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\vol 59
\issue 5
\pages 517--528
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\transl
\jour Algebra and Logic
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\vol 59
\issue 5
\pages 349--356
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    		Алгебра и логика Algebra and Logic
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