Classification of finite commutative semigroups for which the inverse monoid of local automorphisms is permutable.
A semigroup \(S\) is called permutable if any two congruences on \(S\) commute with respect to composition. A local automorphism of a semigroup \(S\) is an isomorphism between two subsemigroups of \(S\). The set of all local automorphisms of \(S\) is an inverse submonoid of the full symmetric inverse monoid on \(S\). The main result of this paper is the following Theorem. Let \(S\) be a commutative semigroup for which the inverse monoid of local automorphisms is permutable. Then \(S\) is either a linearly ordered semilattice, or a primitive semilattice, or an elementary Abelian \(p\)-group or a semigroup with zero multiplication or a nilpotent semigroup of a very special form.
scientific article; zbMATH DE number 6128298