English

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 σ\sigma for the equation x=yx=y can also be defined by σ\sigma-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 xyx\le y.

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}
}
R2 v1 2026-06-22T14:24:14.757Z