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|Title:||Chain varieties of monoids|
|Authors:||Gusev, S. V.|
Vernikov, B. M.
|Publisher:||Institute of Mathematics. Polish Academy of Sciences|
|Citation:||Gusev S. V. Chain varieties of monoids / S. V. Gusev, B. M. Vernikov. — DOI 10.4064/dm772-2-2018 // Dissertationes Mathematicae. — 2018. — Vol. 534. — P. 1-73.|
|Abstract:||A variety of universal algebras is called a chain variety if its subvariety lattice is a chain. Non-group chain varieties of semigroups were completely classified by Sukhanov in 1982. Here we completely determine non-group chain varieties of monoids (referring to monoid varieties, we consider monoids as algebras with an associative binary operation and the nullary operation that fixes the identity element). Even though the lattice of all monoid varieties embeds into the lattice of all semigroup varieties, surprisingly, the classification of non-group chain varieties in the monoid case turns out to be much more complicated than in the case of semigroups. © by Instytut Matematyczny PAN, Warszawa 2018.|
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|Appears in Collections:||Научные публикации, проиндексированные в SCOPUS и WoS CC|
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