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Title: On the lattice of overcommutative varieties of monoids
Authors: Gusev, S. V.
Issue Date: 2018
Publisher: Pleiades Publishing
Citation: Gusev S. V. On the lattice of overcommutative varieties of monoids / S. V. Gusev. — DOI 10.3103/S1066369X18050043 // Russian Mathematics. — 2018. — Vol. 62. — Iss. 5. — P. 23-26.
Abstract: We study the lattice of varieties of monoids, i.e., algebras with two operations, namely, an associative binary operation and a 0-ary operation that fixes the neutral element. It was unknown so far, whether this lattice satisfies some non-trivial identity. The objective of this paper is to give the negative answer to this question. Namely, we prove that any finite lattice is a homomorphic image of some sublattice of the lattice of overcommutative varieties of monoids (i.e., varieties that contain the variety of all commutative monoids). This implies that the lattice of overcommutative varieties of monoids, and therefore, the lattice of all varieties of monoids does not satisfy any non-trivial identity. © Allerton Press, Inc., 2018.
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85048925630
PURE ID: 7282036
ISSN: 1066369X
DOI: 10.3103/S1066369X18050043
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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