偏序集上的局部弱极大理想  

Locally Weak Maximal Ideals on Posets

作　　者：蔡锦[1] 姜广浩[1] 韩贵文[1] 

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000

出　　处：《淮北师范大学学报（自然科学版）》2011年第4期1-5,共5页Journal of Huaibei Normal University：Natural Sciences

基　　金：国家自然科学基金资助项目(11001001;10971092);安徽省教育厅自然科学基金资助项目(KJ2009B001;KJ2009A050Z);淮北师范大学信息学院项目(2010xxjy013)

摘　　要：文章在偏序集上引入并考察局部弱极大理想,给出偏序集上的局部弱极大理想的存在性定理和偏序集上弱理想的一个分解定理,特别地,在满足弱理想降链条件的偏序集上弱理想的一个分解定理.这些定理推广有关文献中的相关结果.In this paper, locally weak maximal ideals on posets are introduced and examined, and the existence of locally weak maximal ideals on posets is proved. The following theorem is obtained： every weak ideal of posets can be decomposed as intersection of some locally weak maximal ideals. Specially, in the posets with discending chain condition of weak ideals, every weak ideal can be decomposed as finite intersection of locally weak maximal ideals. These theorems generalize corresponding results in related references.

关 键 词：偏序集 弱理想 弱极大理想 局部弱极大理想 弱素理想 分解 

分 类 号：O153.3[理学—数学]