On the semigroups with very good magnifiers (Q2709039)

An element \(a\) in a semigroup \(S\) is a left magnifier of \(S\) if the inner left translation \(\lambda_a\) induced by \(a\) is surjective but not injective. If \(a\) is a left magnifier in \(S\), there exists a proper subset \(M\) of \(S\) such that \(M\cap\lambda^{-1}_a(s)\) is a singleton for each \(s\in S\). The set \(M\) is referred to as a minimal subset for the left magnifier \(a\). The left magnifier \(a\) is referred to as a good left magnifier of \(S\) if such a set \(M\) is a subsemigroup of \(S\) and if it is right ideal of \(S\), then \(a\) is referred to as a very good left magnifier of \(S\). Semigroups with very good left manifiers are characterized and a number of their properties are given. For example, their minimal right ideals are determined and conditions are given under which two such semigroups are isomorphic.NEWLINENEWLINEFor the entire collection see [Zbl 0954.00028].