검색
Article Search

JMB Journal of Microbiolog and Biotechnology

OPEN ACCESS eISSN 0454-8124
pISSN 1225-6951
QR Code

Article

Kyungpook Mathematical Journal 2020; 60(3): 455-465

Published online September 30, 2020

Copyright © Kyungpook Mathematical Journal.

Purities of Ordered Ideals of Ordered Semirings

Pakorn Palakawong na Ayutthaya, Bundit Pibaljommee*

Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
e-mail : pakorn1702@gmail.com
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand Centre of Excellence in Mathematics CHE, Bangkok, 10400, Thailand
e-mail : banpib@kku.ac.th

Received: October 30, 2019; Revised: April 2, 2020; Accepted: April 21, 2020

Abstract

We introduce the concepts of the left purity, right purity, quasi-purity, bipurity, left weak purity and right weak purity of ordered ideals of ordered semirings and use them to characterize regular ordered semirings, left weakly regular ordered semirings, right weakly regular ordered semirings and fully idempotent ordered semirings.

Keywords: pure ordered ideal, ordered semiring, regular ordered semiring