剩余格的TL-滤子与TL-同余关系  

TL-filters and TL-congruences of residuated lattices

作　　者：刘熠[1,2] 徐扬[2] 秦晓燕[2] 秦亚[3] 

机构地区：[1]内江师范学院四川省高等学校数值仿真重点实验室,四川内江641112 [2]西南交通大学智能控制开发中心,四川成都610031 [3]内江师范学院数学与信息科学学院,四川内江641112

出　　处：《山东大学学报（理学版）》2012年第2期98-103,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(60875034);四川省教育厅科研基金资助项目(11ZB023)

摘　　要：将有界格上的t-模T应用于剩余格的滤子和同余上,提出了剩余格的TL-滤子与TL-同余关系。首先,研究TL-滤子与TL-同余的性质与一些等价刻画。得到了TL-滤子的集合与TL-同余关系的集合是同构的。最后研究了剩余格的商结构与同态定理,这些理论在其他逻辑代数系统中依然成立。t-norm T of bounded lattices is applied to filters and congruences in residuated lattices,and the concept of TL-filters and TL-congruences of a residuated lattice are introduced.Their properties and some equivalent characterizations are derived.We prove that there is a correspondent bijection between the set of all TL-filters of a residuated lattice and the set of all TL-congruences in that residuated lattice.Finally,quotient residuated lattices and homomorphism theorem are derived.These results and methods still hold in other logical algebraic structures.

关 键 词：剩余格 TL-滤子 TL-同余关系 

分 类 号：O141.1[理学—数学]