Chain varieties of monoids

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 as algebras of tyoe (2,0).

76 pages, 3 figures, 3 tables. In comparison with the previous version, we made a number of linguistic corrections only

Cited by in corpus (14)

• The lattice of varieties of monoids
• Varieties of monoids with complex lattices of subvarieties
• Classification of limit varieties of J-trivial monoids
• Two weaker variants of congruence permutability for monoid varieties
• Limit varieties of aperiodic monoids with commuting idempotents
• Cancellable elements of the lattice of monoid varieties
• Varieties of aperiodic monoids with central idempotents whose subvariety lattice is distributive
• Small monoids generating varieties with uncountably many subvarieties
• Cross varieties of aperiodic monoids with commuting idempotents
• Varieties of aperiodic monoids with commuting idempotents whose subvariety lattice is distributive
• Varieties of monoids with a distributive subvariety lattice
• Minimal monoids generating varieties with complex subvariety lattices
• Distributive and lower-modular elements of the lattice of monoid varieties
• Cross varieties of aperiodic monoids