关于剩余格的理想

J4 ›› 2010, Vol. 45 ›› Issue (4): 66-71.

关于剩余格的理想

刘春辉¹,徐罗山²

1. 赤峰学院初等教育学院, 内蒙古赤峰 024001; 2. 扬州大学数学科学学院, 江苏扬州 225002

收稿日期:2009-06-02 出版日期:2010-04-10 发布日期:2010-05-19
作者简介:刘春辉(1982-),男,硕士,讲师,研究方向为非经典数理逻辑,Domain理论与拓扑学. Email: chunhuiliu1982@163.com
基金资助:
国家自然科学基金资助项目(10371106;60774073)

On ideals of residuated lattices

LIU Chun-hui¹, XU Luo-shan²

1. College of Elementary Education, Chifeng University, Chifeng 024001, Inner Mongolia, China;
2. Section of Mathematics Science, Yangzhou University, Yangzhou 225002, Jiangsu, China

Received:2009-06-02 Online:2010-04-10 Published:2010-05-19

摘要/Abstract

摘要：

研究了剩余格的理想,给出了理想的一些基本性质并利用理想的概念在剩余格上构造了一个同余关系,证明了一个剩余格在该同余关系下的商代数还是剩余格，获得正则剩余格上理想的若干等价刻画定理。

关键词: 剩余格;正则剩余格;理想;同余关系;刻画定理

Abstract:

The ideals in residuated lattice are studied. Some properties of ideals are given, and a congruence relation is structured based on the notion of ideals in residuated lattice. It is proved that the quotient algebra of a residuated lattice under this congruence relation is also a residuated lattice. Some characterization theories of ideals in regular residuated lattice are obtained.

Key words: residuated lattices; regular residuated lattices; ideals; congruence relation; characterization theory

刘春辉1,徐罗山2. 关于剩余格的理想[J]. J4, 2010, 45(4): 66-71.

LIU Chun-hui1, XU Luo-shan2. On ideals of residuated lattices[J]. J4, 2010, 45(4): 66-71.

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