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

Authors : Baddi Ul Zaman

Pages : 1039-1059

Doi:10.15672/hujms.1189391

View : 171 | Download : 222

Publication Date : 2024-08-27

Article Type : Research Paper

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 Greens relations, left P Ehresmann semigroup, right Ehresmann semigroup, Zappa Szép product