m-半格的模糊理想  

Fuzzy ideals of m-semilattices

作　　者：周欣[1] 赵彬[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《西北大学学报（自然科学版）》2015年第2期202-206,共5页Journal of Northwest University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(11171196;11301316);中央高校基本科研业务费专项基金资助项目(GK201302003)

摘　　要：通过模糊集理论的方法,给出了m-半格的(素)模糊理想的概念,讨论了(素)模糊理想和(素)理想之间的关系,研究了模糊理想之集的性质。给出了(素)模糊理想和(素)理想的等价刻画,证明了含最小元的正序m-半格的像集中含1的模糊理想之集是分配l-半群。提出的方法能较好地阐述出模糊集理论与m-半格的联系。By using the fuzzy set method, the concept of （prime） fuzzy ideals of an m-semilattice was introduced, the relationships between （prime） fuzzy ideals and （prime） ideals were discussed and the properties of the sets of all fuzzy ideals were studied. Equivalent characterizations of （prime） fuzzy ideals and （prime） ideals were given, and it is proved that the set of all fuzzy ideals with 1 in their images of a positive m-semilatrice with a bottom element is a distributive 1-semigroup. The link between fuzzy set theory and m-semilattices can be well revealed.

关 键 词：m-半格 (素)理想 (素)模糊理想 

分 类 号：O153.1[理学—数学]