Classification of finite nilsemigroups for which the inverse monoid of local automorphisms is permutable semigroup

  • V. D. Derech

Abstract

A semigroup $S$ is called permutable if $\rho \circ \sigma = \sigma \circ \rho$ for any pair of congruences $\rho$, $\sigma$ on $S$. A local automorphism of the semigroup $S$ is defined as an isomorphism between two subsemigroups of this semigroup. The set of all local automorphisms of a semigroup $S$ with respect to an ordinary operation of composition of binary relations forms an inverse monoid of local automorphisms. In the proposed paper, we present a classification of all finite nilsemigroups for which the inverse monoid of local automorphisms is permutable. Полугруппа $S$ называется перестановочной, если для любой пары конгруэнций $\rho$, $\sigma$ на $S$ имеет место равенство $\rho \circ \sigma = \sigma \circ \rho$.
Published
25.05.2016
How to Cite
Derech, V. D. “Classification of Finite Nilsemigroups for Which the Inverse Monoid of Local Automorphisms Is Permutable Semigroup”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, no. 5, May 2016, pp. 610-24, http://umj.imath.kiev.ua/index.php/umj/article/view/1865.
Section
Research articles