Mathematics Faculty Articles

Title

Equational Theories of Unstable Involution Semigroups

Document Type

Article

Publication Date

3-24-2017

Publication Title

Electronic Research Announcements in Mathematical Sciences

Keywords

Semigroup, Involution, Unstable, Identity, Basis, Infinite basis problem

ISSN

1935-9179

Volume

24

First Page

10

Last Page

20

Abstract

It is long known that with respect to the property of having a finitely axiomatizable equational theory, there is no relationship between a general involution semigroup and its semigroup reduct. The present article establishes such a relationship within the class of involution semigroups that are unstable in the sense that the varieties they generate contain semilattices with nontrivial involution. Specifically, it is shown that the equational theory of an unstable involution semigroup is not finitely axiomatizable whenever the equational theory of its semigroup reduct satisfies the same property. Consequently, many results on equational properties of semigroups can be converted into results applicable to involution semigroups.

Comments

©2016 American Institute of Mathematical Sciences

ORCID ID

0000-0002-1662-3734

ResearcherID

I-6970-2013

DOI

10.3934/era.2017.24.002

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