剩余格的TL-滤子与TL-同余关系

J4 ›› 2012, Vol. 47 ›› Issue (2): 98-103.

剩余格的TL-滤子与TL-同余关系

刘熠^1,2,徐扬²,秦晓燕²,秦亚³

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

收稿日期:2011-01-27 出版日期:2012-02-20 发布日期:2012-12-24
作者简介:刘熠(1979- ),男,博士研究生,讲师,研究方向为逻辑代数、代数逻辑以及智能信息处理. Email:liuyiyl@126.com
基金资助:
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)

TL-filters and TL-congruences of residuated lattices

LIU Yi^1,2, XU Yang², QIN Xiao-yan², QIN Ya³

1. Key Laboratory of Numerical Simulation in the Sichuan Provincial College, Neijiang Normal University,
Neijiang 641112, Sichuan, China;
2. Intelligent Control Development Center, Southwest Jiaotong University, Neijiang 610031, Sichuan, China;
3. College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641112, Sichuan, China

Received:2011-01-27 Online:2012-02-20 Published:2012-12-24

摘要/Abstract

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。

关键词: 剩余格;TL-滤子;TL-同余关系

Abstract:

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.

Key words: residuated lattices; TL-filters; TL-congruences

刘熠1,2,徐扬2,秦晓燕2,秦亚3. 剩余格的TL-滤子与TL-同余关系[J]. J4, 2012, 47(2): 98-103.

LIU Yi1,2, XU Yang2, QIN Xiao-yan 2, QIN Ya3. TL-filters and TL-congruences of residuated lattices[J]. J4, 2012, 47(2): 98-103.

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