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.
| Original language | American English |
|---|---|
| Pages (from-to) | 399–411 |
| Journal | Houston Journal of Mathematics |
| Volume | 44 |
| Issue number | 2 |
| State | Published - Jan 1 2018 |
Bibliographical note
Publisher Copyright:© 2018 University of Houston
ASJC Scopus Subject Areas
- General Mathematics
Keywords
- Identity
- Basis
- Irredundant basis
- Semigroup
- Involution semigroup
Disciplines
- Mathematics
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