Identities in full transformation semigroups
Let \(L\) be a finite alphabet and let \(L^*\) denote the free monoid over \(L\). The authors show that if two words \(V, W \in L^*\) satisfy certain conditions, then there is an identity involving \(V\) and \(W\), which holds in every proper subsemigroup of \(H_ n\), the semigroup of all selfmaps of the set of \(n\) elements, but not in \(H_ n\) itself. They then go on to provide several constructions of words \(V\) and \(W\) which satisfy the required conditions.
scientific article; zbMATH DE number 638598