COMPLETELY PRIME IDEALS OF SEMIGROUPS

Bajrami, Merita and Ramani-Halili, Rushadije (2020) COMPLETELY PRIME IDEALS OF SEMIGROUPS. Journal of Natural Sciences and Mathematics of UT.

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Abstract

In this paper we discuss a very useful tool in the study of semigroup theory, called completely prime ideals. We will study characterization of semilattice congruences by means of completely prime ideals. We will follow the procedure of finding all subdirectly irreducible semilattices, then construct all congruences induced by homomorphism onto these, and finally take arbitrary intersections of congruences constructed. The usual algebraic books and papers studied semilattice congruence of semigroups by means of strongly prime ideals. We give some necessary and sufficient conditions about completely semiprime ideals, semilattice congruence and filters, which provide clearer informations about semigroups structure and new algebraic approach of studying them. Also we study the relationship between -simple semigroup and completely prime ideals. So the purpose of this paper is two-fold: to characterize an arbitrary nonempty intersection of completely prime ideals and characterize subsets which are congruence classes of some semilattice congruence.

Item Type: Article
Subjects: Q Science > Q Science (General)
Q Science > QA Mathematics
Divisions: Faculty of Engineering, Science and Mathematics > School of Mathematics
Depositing User: Unnamed user with email zshi@unite.edu.mk
Date Deposited: 14 Nov 2020 22:38
Last Modified: 06 Dec 2020 19:32
URI: http://eprints.unite.edu.mk/id/eprint/618

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