# Structure of a finite commutative inverse semigroup and a finite bundle for which the inverse monoid of local automorphisms is permutable

### Abstract

For a semigroup $S$, the set of all isomorphisms between subsemigroups of $S$ is an inverse monoid with respect to composition, which is denoted by $P A(S)$ and is called the monoid of local automorphisms of $S$. A semigroup $S$ is called permutable if, for any pair of congruences $p, \sigma$ on $S$, one has $p \circ \sigma = \sigma \circ p$. We describe the structure of a finite commutative inverse semigroup and a finite band whose monoids of local automorphisms are permutable.
Published

25.09.2011

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 63, no. 9, Sept. 2011, pp. 1218-26, https://umj.imath.kiev.ua/index.php/umj/article/view/2799.

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Section

Research articles