Authors: RIDA E ZENAB

Abstract: In this article we discuss the factorisations of semigroups and monoids in the context of direct, semidirect and Zappa-Szep products addressing the question of uniqueness. An equivalence between external and internal Zappa-Szep product of groups and monoids is known, but no such correspondence exists for semigroups in general. We prove the equivalence between external and internal Zappa-Szep product of semigroups subject to certain conditions in this article. We end with some illustrative examples of the Zappa-Szep product of the bisimple inverse monoids.

Keywords: Zappa-Szep products, semigroups, bisimple inverse monoids

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