Classification of Finite Commutative Semigroups for Which the Inverse Monoid of Local Automorphisms is a ∆-Semigroup - Derech, V. D. (Ukrains’kyi Matematychnyi Zhurnal, 2015)
A semigroup S is called a ∆-semigroup if the lattice of its congruences forms a chain relative to the inclusion. A local automorphism of the semigroup S> is called an isomorphism between its two subsemigroups. The set of all local automorphisms of the semigroup S relative to the ordinary operation of composition of binary relations forms an inverse monoid of local automorphisms. We present a classification of finite commutative semigroups for which the inverse monoid of local automorphisms is a ∆-semigroup.