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