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
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Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand Centre of Excellence in Mathematics CHE, Bangkok, 10400, Thailand
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Received: October 30, 2019; Revised: April 2, 2020; Accepted: April 21, 2020
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