Open AccessOn left restriction semigroups with zero
Author(s) -
Baddi-Ul Zaman
Publication year - 2022
Publication title -
maǧallaẗ al-kuwayt li-l-ʿulūm
Language(s) - English
Resource type - Journals
eISSN - 2307-4116
pISSN - 2307-4108
DOI - 10.48129/kjs.16921
Subject(s) - semigroup , mathematics , zero (linguistics) , monoid , pure mathematics , ideal (ethics) , special classes of semigroups , set (abstract data type) , transformation (genetics) , discrete mathematics , combinatorics , computer science , philosophy , linguistics , biochemistry , chemistry , epistemology , gene , programming language
In this article, we give the notion of left restriction meet-semigroup, and establish some results regarding atomistic left restriction semigroups. Then we discuss decompositions of (non-zero) semigroups with zero by proving a decomposition theorem. We also show that every atomistic left restriction semigroup S can be decomposed as an orthogonal sum of atomistic left restriction semigroups Ni, where each summand Ni is an irreducible ideal of S. Finally, properties of the summands Ni, when S embeds in some PT X the partial transformation monoid on a set X, are investigated.