Special elements of the lattice of monoid varieties

Abstract

We completely classify all neutral or costandard elements in the lattice $\mathbb{MON}$ of all monoid varieties. Further, we prove that an arbitrary upper-modular element of $\mathbb{MON}$ except the variety of all monoids is either a completely regular or a commutative variety. Finally, we verify that all commutative varieties of monoids are codistributive elements of $\mathbb{MON}$. Thus, the problems of describing codistributive or upper-modular elements of $\mathbb{MON}$ are completely reduced to the completely regular case.

12 pages

References in corpus (1)

• On the lattice of overcommutative varieties of monoids

Cited by in corpus (4)

• The lattice of varieties of monoids
• Two weaker variants of congruence permutability for monoid varieties
• Cancellable elements of the lattice of monoid varieties
• Standard elements of the lattice of monoid varieties