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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 7, pp. 867–873, July, 2015.
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Derech, V.D. Classification of Finite Commutative Semigroups for Which the Inverse Monoid of Local Automorphisms is a ∆-Semigroup. Ukr Math J 67, 981–988 (2015). https://doi.org/10.1007/s11253-015-1130-0
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DOI: https://doi.org/10.1007/s11253-015-1130-0