Cancellable elements of the lattice of semigroup varieties

TL;DR

This paper characterizes all commutative semigroup varieties that are cancellable within the lattice of all semigroup varieties, revealing their equivalence to modular elements.

Contribution

It provides a complete classification of cancellable commutative semigroup varieties and establishes their equivalence to modular elements in the lattice.

Findings

All cancellable commutative semigroup varieties are identified.

Cancellability and modularity are shown to be equivalent properties for these varieties.

Abstract

We completely determine all commutative semigroup varieties that are cancellable elements of the lattice SEM of all semigroup varieties. In particular, we prove that, for commutative varieties, the properties of being cancellable and modular elements of SEM are equivalent.