On bases of identities for the \(\omega\)-variety generated by locally testable semigroups. (Q935166)

The authors treat finite semigroups as algebras of type \((2,1)\) where the additional unary operation \(x\mapsto x^\omega\) maps an element \(s\) of a finite semigroup to the unique idempotent of the subsemigroup generated by \(s\). They consider the variety \(LSI^\omega\) of such algebras generated by finite locally testable semigroups. The authors solve the word problem for the free algebra in \(LSI^\omega\) and give an identity basis for this variety. The basis involves identities in at most 3 variables but is infinite; the authors show that \(LSI^\omega\) has no finite identity basis.