Inverse subsemigroups and classes of finite aperiodic semigroups |
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Authors: | Alexei Vernitski |
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Affiliation: | (1) Department of Mathematical Sciences, University of Essex, Colchester, CO4 3SQ, UK |
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Abstract: | We prove a number of results related to finite semigroups and their inverse subsemigroups, including the following. (1) A finite semigroup is aperiodic if and only if it is a homomorphic image of a finite semigroup whose inverse subsemigroups are semilattices. (2) A finite inverse semigroup can be represented by order-preserving mappings on a chain if and only if it is a semilattice. Finally, we introduce the concept of pseudo-small quasivariety of finite semigroups, generalizing the concept of small variety. |
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Keywords: | Inverse subsemigroup Aperiodic semigroup Semilattice Quasivariety of finite semigroups Semigroup of order-preserving mappings |
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