Identities and quasiidentities in the lattice of overcommutative semigroup varieties

TL;DR

This paper investigates the structure of overcommutative semigroup varieties, showing that the lattice of their subvarieties satisfies a non-trivial identity or quasiidentity, which are proven to be equivalent properties.

Contribution

It characterizes overcommutative semigroup varieties whose subvariety lattices satisfy specific identities or quasiidentities, establishing the equivalence of these properties.

Findings

Identifies conditions under which the lattice satisfies a non-trivial identity.

Proves the equivalence between satisfying an identity and a quasiidentity.

Provides a structural description of overcommutative varieties with these properties.

Abstract

We describe overcommutative varieties of semigroups whose lattice of overcommutative subvarieties satisfies a non-trivial identity or quasiidentity. These two properties turn out to be equivalent.