序半群中的粗糙理想

Rough Ideals in Ordered Semigroups

引入了序半群中(上,下)粗糙理想的概念,讨论了序半群中理想与(上,下)粗糙理想的关系,证明了对含最小元的序半群,若任一元素的等价类是有限的,则下粗糙理想之集关于包含序构成一个代数格。最后,讨论了(半,准)素理想与(上,下)粗糙(半,准)素理想的关系。

In this paper, the notions of （upper, lower） rough ideals of an ordered semigroup are proposed, the relationship between ideals and （upper, lower） rough ideals of an ordered semigroup is discussed, and it is proved that if θ is an equivalence relation on anordered semigroup S with the bottom element and S satisfies ｜[-x]θ [ 〈 ＋∞ for every x ∈ S, then （θ-Id （S）, ） is analgebraic lattice. Finally, the relationship between prime （semi-prime, primary prime） ideals and （upper, lower） rough prime （semi-prime, primary prime） idealsis discussed.