Open AccessEventually Pointed Principally Ordered Regular Semigroups
Author(s) -
Gama Pinto
Publication year - 2020
Publication title -
maǧallaẗ ǧāmiʿaẗ al-sulṭān qābūs li-l-ʿulūm/sultan qaboos university journal for science
Language(s) - English
Resource type - Journals
eISSN - 2414-536X
pISSN - 2308-3921
DOI - 10.24200/squjs.vol24iss2pp139-146
Subject(s) - semigroup , mathematics , simple (philosophy) , subalgebra , integer (computer science) , partially ordered set , element (criminal law) , combinatorics , regular semigroup , pure mathematics , existential quantification , discrete mathematics , special classes of semigroups , algebra over a field , computer science , philosophy , epistemology , law , political science , programming language
An ordered regular semigroup, , is said to be principally ordered if for every there exists . A principally ordered regular semigroup is pointed if for every element, we have . Here we investigate those principally ordered regular semigroups that are eventually pointed in the sense that for all there exists a positive integer, , such that . Necessary and sufficient conditions for an eventually pointed principally ordered regular semigroup to be naturally ordered and to be completely simple are obtained. We describe the subalgebra of generated by a pair of comparable idempotents and such that .