Chain varieties of monoids
Volume 534 / 2018
Dissertationes Mathematicae 534 (2018), 1-73
MSC: Primary 20M07; Secondary 08B15.
DOI: 10.4064/dm772-2-2018
Published online: 15 October 2018
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.
