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.
ZENAB, RIDA E.
"Decompositions of semigroups,"
Turkish Journal of Mathematics: Vol. 45:
6, Article 12.
Available at: https://journals.tubitak.gov.tr/math/vol45/iss6/12