On simple left, right and two-sided ideals of an ordered semigroup having a kernel
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The intersection of all two-sided ideals of an ordered semi- group, if it is non-empty, is called the kernel of the ordered semigroup. A left ideal L of an ordered semigroup (S, ·,) having a kernel I is said to be simple if I is properly contained in L and for any left ideal L′ of (S, ·,), I is properly contained in L′ and L′ is contained in L imply L′ = L. The notions of simple right and two-sided ideals are defined similarly. In this paper, the author characterize when an ordered semigroup having a ker- nel is the class sum of its simple left, right and two-sided ideals. Further, the structure of simple two-sided ideals will be discussed.
Abstract
The intersection of all two-sided ideals of an ordered semi- group, if it is non-empty, is called the kernel of the ordered semigroup. A left ideal L of an ordered semigroup (S, ·,) having a kernel I is said to be simple if I is properly contained in L and for any left ideal L′ of (S, ·,), I is properly contained in L′ and L′ is contained in L imply L′ = L. The notions of simple right and two-sided ideals are defined similarly. In this paper, the author characterize when an ordered semigroup having a ker- nel is the class sum of its simple left, right and two-sided ideals. Further, the structure of simple two-sided ideals will be discussed.
참고문헌 (6)
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