On Finite Complete Presentations and Exact Decompositions of Semigroups
نویسنده
چکیده
We prove that given a finite (zero) exact right decomposition (M, T ) of a semigroup S, if M is defined by a finite complete presentation then S is also defined by a finite complete presentation. Exact right decompositions are natural generalizations to semigroups of coset decompositions in groups. As a consequence we deduce that the Zappa-Szép extension of a monoid defined by a finite complete presentation, by a finite monoid is also defined by such a presentation. It is also shown that when a semigroup A isomorphic to a variant semigroup A(x) that is defined by a finite complete presentation, where x belongs to a sandwich matrix P , together with some other conditions, we deduce that the zero Rees matrix semigroup M0[A; I, J ; P ] is also defined by a finite complete presentation.
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