Weakly Semiprime Segments in Ordered Semigroups

Panuwat Luangchaisri and Thawhat Changphas
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Panuwat Luangchaisri: Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Thawhat Changphas: Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Mathematics, 2019, vol. 7, issue 9, 1-9

Abstract: Let P 2 ⊂ P 1 be a pair of weakly semiprime ideals of an ordered semigroup ( S , · , ≤ ) . Then, the pair P 2 ⊂ P 1 is called a weakly semiprime segment of S if ? n ∈ N I n ⊆ P 2 for all ideals I of S such that P 2 ⊂ I ⊂ P 1 . In this paper, we classify weakly semiprime segments of an ordered semigroup into four types; those that are simple, exceptional, Archimedean, and decomposable.

Keywords: weakly semiprime; prime; segment; ordered semigroup (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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