Saturated (n, m)-Regular Semigroups

The aim of this paper is to determine several saturated classes of structurally regular semigroups. First, we show that structurally (n,m)-regular semigroups are saturated in a subclass of semigroups for any pair (n,m) of positive integers. We also demonstrate that, for all positive integers n and k with 1≤k≤n, the variety of structurally (0,n)-left seminormal bands is saturated in the variety of structurally (0,k)-bands. As a result, in the category of structurally (0,k)-bands, epis from structurally (0,n)-left seminormal bands is onto.