Geodesic
Associative algebras with a distributive lattice of subalgebras
Algebra i logika, Tome 59 (2020) no. 5, pp. 517-528

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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. 
@article{AL_2020_59_5_a0,
     author = {A. G. Gein},
     title = {Associative algebras with a distributive lattice of subalgebras},
     journal = {Algebra i logika},
     pages = {517--528},
     publisher = {mathdoc},
     volume = {59},
     number = {5},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2020_59_5_a0/}
}
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A. G. Gein. Associative algebras with a distributive lattice of subalgebras. Algebra i logika, Tome 59 (2020) no. 5, pp. 517-528. http://geodesic.mathdoc.fr/item/AL_2020_59_5_a0/