Local finiteness for Green's relations in semigroup varieties

TL;DR

This paper characterizes locally Green's relation finite varieties of semigroups with finite axiomatic rank using forbidden objects, advancing understanding of their structural properties.

Contribution

It provides a new characterization of locally K-finite semigroup varieties of finite axiomatic rank through forbidden objects.

Findings

Characterization of locally K-finite varieties using forbidden objects

Applicable to varieties with finite axiomatic rank

Enhances understanding of semigroup structure and Green's relations

Abstract

A semigroup variety V is said to be locally K-finite, where K stands for any of Green's relations H, R, L, D, or J, if every finitely generated semigroup from V has only finitely many K-classes. We characterize locally K-finite varieties of finite axiomatic rank in the language of "forbidden objects".