Mathematics Faculty Articles

Title

On a Class of Completely Join Prime J-Trivial Semigroups with Unique Involution

Document Type

Article

Publication Date

10-2017

Publication Title

Algebra Universalis

Keywords

Semigroup, Involution, Pseudovariety, Completely join prime

ISSN

0002-5240

Volume

78

Issue/No.

2

First Page

131

Last Page

145

Abstract

A finite algebra is completely join prime if whenever it belongs to the complete join of some collection of pseudovarieties, then it belongs to one of the pseudovarieties. An infinite class of completely join prime J-trivial semigroups with unique involution is introduced to demonstrate the incompatibility between the lattice of pseudovarieties of involution semigroups and the lattice of pseudovarieties of semigroups. Examples are also exhibited to show that a finite involution semigroup and its semigroup reduct need not be simultaneously completely join prime.

Comments

©Springer International Publishing 2017

ORCID ID

0000-0002-1662-3734

ResearcherID

I-6970-2013

DOI

10.1007/s00012-017-0442-3

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