Reducibility versus definability for pseudovarieties of semigroups
Group Theory
2019-03-18 v1
Abstract
It is easy to show that a pseudovariety which is reducible with respect to an implicit signature for the equation can also be defined by -identities. We present several negative examples for the converse using signatures in which the pseudovarieties are usually defined. An ordered example issue from the extended Straubing-Th\'erien hierarchy of regular languages is also shown to provide a positive example for the inequality .
Keywords
Cite
@article{arxiv.1606.04059,
title = {Reducibility versus definability for pseudovarieties of semigroups},
author = {J. Almeida and O. Klíma},
journal= {arXiv preprint arXiv:1606.04059},
year = {2019}
}