The rank of variants of nilpotent pseudovarieties

TL;DR

This paper studies the complexity of certain classes of semigroups defined by nilpotency conditions, providing finite bases for some and showing others lack finite rank, advancing understanding of their algebraic structure.

Contribution

It introduces finite bases for several nilpotent pseudovarieties and proves the Neumann-Taylor variant has infinite rank, highlighting differences among variants.

Findings

Finite bases established for several nilpotent pseudovarieties

Neumann-Taylor variant does not have finite rank

Advances understanding of algebraic structure of nilpotent variants

Abstract

We investigate the rank of pseudovarieties defined by several of the variants of nilpotency conditions for semigroups in the sense of Mal'cev. For several of them, we provide finite bases of pseudoidentities. We also show that the Neumann-Taylor variant does not have finite rank.