On left $P$-Ehresmann and right Ehresmann semigroups: $\lambda$-semidirect products and Zappa-Szép products

Year 2024, Volume: 53 Issue: 4, 1039 - 1059, 27.08.2024

Baddi Ul Zaman

https://doi.org/10.15672/hujms.1189391

Abstract

We show that the $\lambda$-semidirect product $M \rtimes^{\lambda} W$ of a left $P$-Ehresmann semigroup $M$ and a left restriction semigroup $W$ is a left $P$-Ehresmann semigroup. We explore the behavior of generalized Green's relations on $M \rtimes^{\lambda} W$, and investigate some properties of $M \rtimes^{\lambda} W$. Then the Zappa-Szép product of a right Ehresmann semigroup and its distinguished semilattice is studied. An example of Zappa-Szép product in the context of right Ehresmann semigroups is also given.

Keywords

generalized Green’s relations, left P-Ehresmann semigroup, right Ehresmann semigroup, Zappa-Szép product

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