Epimorphisms, dominions and seminormal identities. (Q972591)

Let \(S\) be a semigoup. Then a subsemigroup \(U\) of \(S\) is called dense if the inclusion is an epimorphism. We say that a system \(\Phi\) of semigroup identities is preserved under epis if for every semigroup \(U\) satisfying \(\Phi\) every semigroup \(S\) such that \(U\) is a dense subsemigroup of \(S\) satisfies also \(\Phi\). The aim of the author is to characterize systems of semigroup identities preserved under epis. This paper gives some sufficient conditions for a system of semigroup identities containing a seminormal permutation identity to be preserved under epis.