Finiteness properties of varieties and the restriction to finite semigroups.

Speaker: Marcel Jackson, LaTrobe University

Abstract: Mark Sapir showed that a finite semigroup has a finite basis for its identities if and only if it does so within the class of finite semigroups. We look at corresponding questions for other finiteness conditions on varieties. For example, we find that there is a finitely generated semigroup variety containing uncountably many subvarieties with no finite equational basis, but such that all finitely generated subvarieties are finitely based (hence the so-called "hereditarily finitely based" property is not equivalent to its restriction to finitely generated varieties).