## Mathematics Faculty Articles

# A Sufficient Condition for the Absence of Irredundant Bases

## Document Type

Article

## Publication Date

2018

## Publication Title

Houston Journal of Mathematics

## ISSN

0362-1588

## Volume

44

## Issue/No.

2

## First Page

399

## Last Page

411

## Abstract

A basis of identities for an algebra is *irredundant* if each of its proper subsets fails to be a basis. A sufficient condition is established under which a non-finitely based finite algebra of finite type has no irredundant bases. This result is then used to construct the first known trio of finite involution semigroups, all sharing a common semigroup reduct, such that one has a finite basis, one has an infinite irredundant basis, and one has no irredundant bases.

## NSUWorks Citation

Lee, Edmond W. H., "A Sufficient Condition for the Absence of Irredundant Bases" (2018). *Mathematics Faculty Articles*. 256.

https://nsuworks.nova.edu/math_facarticles/256