The regular part of a semigroup of transformations with restricted range.
Let \(X\) be a set and \(T(X)\) the semigroup of all transformations of \(X\). For \(Y\subset X\) let \(F(X,Y)\) be the subsemigroup consisting of all transformations \(f\) satisfying \(f(X)=f(Y)\subset Y\). In the paper under review the author describes Green's relations and ideals of \(F(X,Y)\). As a corollary, in the case of non-empty finite \(Y\) the author describes all maximal regular subsemigroups of \(F(X,Y)\). Furthermore, the authors determines all cases in which \(F(X,Y)\) is isomorphic to the full transformation semigroup on some set and shows that every regular semigroup \(S\) embeds into \(F(S^1,S)\).
scientific article; zbMATH DE number 6018058