偏序集上的局部极大理想  

Locally Maximal Ideals on Posets

作　　者：姜广浩[1] 王戈平[2] 

机构地区：[1]南京大学数学系,江苏南京210093 [2]徐州师范大学数学系,江苏徐州221116

出　　处：《徐州师范大学学报（自然科学版）》2006年第1期11-14,共4页Journal of Xuzhou Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10371079)

摘　　要：在偏序集上引入并考察了偏序集上的局部极大理想,证明了偏序集上的局部极大理想的存在性定理和偏序集上理想的分解定理,特别地,在满足理想降链条件的偏序集上理想的分解定理.In this paper,the locally maximal ideals on posets are introduced and examined. The existence of locally maximal ideals on posets is proved,and the following theorem is obtained. Every ideal of posets can be decomposed as intersection of some locally maximal ideals. Specially, in the posets with discending chain condition of ideals,every ideal can be decomposed as finite intersection of locally maximal ideals.

关 键 词：偏序集 局部极大理想 分解 

分 类 号：O189.1[理学—数学] O153.1[理学—基础数学]