Geodesic
Associative algebras with a distributive lattice of subalgebras
Algebra i logika, Tome 59 (2020) no. 5, pp. 517-528 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {A. G. Gein},
     title = {Associative algebras with a distributive lattice of subalgebras},
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     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/

[1] O. Ore, “Structures and group theory. II”, Duke Math. J., 4:2 (1938), 247–269 | DOI | MR

[2] L. N. Shevrin, “Polugruppy s nekotorymi tipami struktur podpolugrupp”, Dokl. AN SSSR, 138:4 (1961), 796–798 | Zbl

[3] P. A. Freidman, “Koltsa s distributivnoi strukturoi podkolets”, Matem. sb., 73(115):4 (1967), 513–534

[4] A. G. Gein, “Distributivnyi zakon v reshetke podlalgebr”, Serdika B'lgarsko matem. spis., 11 (1985), 171–179 | MR

[5] D. W. Barnes, “Lattice isomorphisms of associative algebras”, J. Aust. Math. Soc., 6:1 (1966), 106–121 | DOI | MR | Zbl

[6] N. Dzhekobson, Stroenie kolets, IL, M., 1961

[7] A. G. Gein, “Ob assotsiativnykh algebrakh s distributivnoi reshetkoi podalgebr”, Mezhd. konf. "‘Maltsevskie chteniya"’, Tez. dokl. (19–22 noyabrya 2018, Novosibirsk), IM SO RAN i NGU, Novosibirsk, 2018, 146 http://math.nsc.ru/conference/malmeet/18/maltsev18.pdf