关于偏序半群的素理想与弱素理想

On Prime, Weakly Prime Ideals of Ordered Semigroups

引入ｍ－系（ｎ－系）的概念，通过它们刻划了偏序半群的弱素理想（弱半素理想），同时证明了它们及素理想的几个重要性质．这些性质和环论及一般半群的有关结论很相似．作为应用，这些结论在一般半群中都成立．

Some characterizations of weakly prime ideals of ordered semigrouups are obtained by m-system and those of weakly semiprime ideals by n-system. Some interesting properties of prime ideals, weakly prime ideals of ordered semigroups are given, and they are analogous to those conclusions about rings and semigroups. As an application of the results of this paper, all results in this paper are true in semigroups.