Distributive and Lower-Modular Elements of the Lattice of Monoid Varieties
Sergey V. Gusev · Siberian Mathematical Journal · 2022
In the lattice of semigroup varieties, the set of all neutral elements is finite, the set of all distributive elements is countably infinite, and the set of all lower-modular elements is uncountably infinite. It was established in 2018 that the lattice of monoid varieties contains exactly three neutral elements. This article shows that neutrality, distributivity, and lower-modularity coincide in the lattice of monoid varieties. Thus, there exists only three varieties that are distributive and lower-modular elements of this lattice.