Two weaker variants of congruence permutability for monoid varieties

Abstract

We completely determine all varieties of monoids on whose free objects all fully invariant congruences or all fully invariant congruences contained in the least semilattice congruence permute. Along the way, we find several new monoid varieties with the distributive subvariety lattice (only a few examples of varieties with such a property are known so far).

41 pages

References in corpus (1)

• Standard elements of the lattice of monoid varieties

Cited by in corpus (4)

• The lattice of varieties of monoids
• Cancellable elements of the lattice of monoid varieties
• Varieties of aperiodic monoids with central idempotents whose subvariety lattice is distributive
• Minimal monoids generating varieties with complex subvariety lattices