Weakly Semiprime Segments in Ordered Semigroups

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