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.
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A. G. Gein, “Associative algebras with a distributive lattice of subalgebras,” Mal’tsev Readings (2018), p. 146; http://math.nsc.ru/conference/malmeet/18/maltsev18.pdf.
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Translated from Algebra i Logika, Vol. 59, No. 5, pp. 517-528, September-October, 2020. Russian https://doi.org/10.33048/alglog.2020.59.501.
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).
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Gein, A.G. Associative Algebras with a Distributive Lattice of Subalgebras. Algebra Logic 59, 349–356 (2020). https://doi.org/10.1007/s10469-020-09608-6
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DOI: https://doi.org/10.1007/s10469-020-09608-6