Associative Algebras with a Distributive Lattice of Subalgebras

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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Bibliographic Details
Published in:Algebra and logic 2020-11, Vol.59 (5), p.349-356
Main Author: Gein, A. G.
Format: Article
Language:English
Subjects:
Algebra
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
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Description
Summary: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.
ISSN:0002-5232
1573-8302
DOI:10.1007/s10469-020-09608-6