2017
Том 69
№ 9

All Issues

Classification of Finite Commutative Semigroups for Which the Inverse Monoid of Local Automorphisms is a ∆-Semigroup

Derech V. D.


Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 7, pp 981-988.

Citation Example: Derech V. D. Classification of Finite Commutative Semigroups for Which the Inverse Monoid of Local Automorphisms is a ∆-Semigroup // Ukr. Mat. Zh. - 2015. - 67, № 7. - pp. 867-873.