Some operators that preserve the locality of a pseudovariety of semigroups

TL;DR

This paper investigates how certain operators preserve the locality property of pseudovarieties of semigroups, providing new insights into their structural behavior and interactions.

Contribution

It demonstrates that specific operators maintain locality in monoidal pseudovarieties and explores their interactions with other operators, advancing the understanding of pseudovariety transformations.

Findings

Operators K(m)V, D(m)V, and LI(m)V preserve locality.

Results on the interplay between Z(m)(_) and (_)*D_k operators.

New conditions under which locality is preserved by these operators.

Abstract

It is shown that if V is a local monoidal pseudovariety of semigroups, then K(m)V, D(m)V and LI(m)V are local. Other operators of the form Z(m)(_) are considered. In the process, results about the interplay between operators Z(m)(_) and (_)*D_k are obtained.