Endomorphisms of the lattice of epigroup varieties
Group Theory
2020-01-22 v6
Abstract
We examine varieties of epigroups as unary semigroups, that is semigroups equipped with an additional unary operation of pseudoinversion. The article contains two main results. The first of them indicates a countably infinite family of injective endomorphisms of the lattice of all epigroup varieties. An epigroup variety is said to be a variety of finite degree if all its nilsemigroups are nilpotent. The second result of the article provides a characterization of epigroup varieties of finite degree in a language of identities and in terms of minimal forbidden subvarieties. Note that the first result is essentially used in the proof of the second one.
Keywords
Cite
@article{arxiv.1404.0478,
title = {Endomorphisms of the lattice of epigroup varieties},
author = {S. V. Gusev and B. M. Vernikov},
journal= {arXiv preprint arXiv:1404.0478},
year = {2020}
}
Comments
In comparison with the previous version, we eliminate a few typos only