A Bijection between Lattice-Valued Filters and Lattice-Valued Congruences in Residuated Lattices

被引：27

作者：

Wei, Wei ^{[1
]}

Qiang, Yan ^{[2
]}

Zhang, Jing ^{[1
]}

机构：

[1] Xian Univ Technol, Sch Comp Sci & Engn, Xian 710048, Shaanxi, Peoples R China

[2] Taiyuan Univ Technol, Coll Comp Sci & Technol, Taiyuan 030024, Peoples R China

来源：

MATHEMATICAL PROBLEMS IN ENGINEERING | 2013年 / 2013卷

基金：

中国国家自然科学基金;

关键词：

LOGIC;

D O I：

10.1155/2013/908623

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

The aim of this paper is to study relations between lattice-valued filters and lattice-valued congruences in residuated lattices. We introduce a new definition of congruences which just depends on the meet. and the residuum ->. Then it is shown that each of these congruences is automatically a universal-algebra-congruence. Also, lattice-valued filters and lattice-valued congruences are studied, and it is shown that there is a one-to-one correspondence between the set of all (lattice-valued) filters and the set of all (lattice-valued) congruences.

引用

页数：6

共 17 条

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