On identities of indicator burnside semigroups

TL;DR

This paper investigates indicator Burnside semigroups, proving they have polynomially decidable equational theories and generate finitely based varieties, thereby advancing understanding of Rees-Sushkevich varieties in semigroup theory.

Contribution

It establishes that indicator Burnside semigroups have polynomially decidable equational theories and generate finitely based varieties, clarifying their role in the structure of Rees-Sushkevich varieties.

Findings

Indicator Burnside semigroups have polynomially decidable equational theories.

Each indicator Burnside semigroup generates a finitely based variety.

Characterization of Rees-Sushkevich varieties via indicator Burnside semigroups.

Abstract

A semigroup variety is said to be a Rees-Sushkevich variety if it is contained in a periodic variety generated by 0-simple semigroups. S. I. Kublanovsky has proven that a variety V is a Rees-Sushkevich variety if and only it does not contain any of special finite semigroups. These semigroups are called indicator Burnside semigroups. It is shown that indicator Burnside semigroups have polynomially decidable equational theory. Also it is shown that each indicator Burnside semigroups generate a finitely based variety.