关于剩余格中滤子的格结构

数学季刊 ›› 2009, Vol. 24 ›› Issue (2): 252-257.

关于剩余格中滤子的格结构

1. Department of Mathematics, Hebi Vocational Technical College2. College of Education, Nanyang Institute of Technology

收稿日期:2005-12-26 出版日期:2009-06-30 发布日期:2023-07-24
作者简介:ZHANG Xiao-hua(1958-), female, native of Dianjiang, Sichuan, an associate professor of Hebi Vocational Technical College, engages in mathematics teaching.

On Lattice Structure of Filters in Residuated Lattices

1. Department of Mathematics, Hebi Vocational Technical College2. College of Education, Nanyang Institute of Technology

Received:2005-12-26 Online:2009-06-30 Published:2023-07-24
About author:ZHANG Xiao-hua(1958-), female, native of Dianjiang, Sichuan, an associate professor of Hebi Vocational Technical College, engages in mathematics teaching.

摘要/Abstract

摘要： This paper is devoted to the discussion of filters in residuated lattices. The lattice structure of filters in residuated lattice was established. It is proved that the set of all filters forms a distributive lattice. Also, the concept of prime filter in residuated lattice was proposed and some equivalent conditions about prime filter were given.

关键词: residuated lattice, MTL-algebra, filter, prime filter

Abstract: This paper is devoted to the discussion of filters in residuated lattices. The lattice structure of filters in residuated lattice was established. It is proved that the set of all filters forms a distributive lattice. Also, the concept of prime filter in residuated lattice was proposed and some equivalent conditions about prime filter were given.

Key words: residuated lattice, MTL-algebra, filter, prime filter

中图分类号:

O153.1

张晓华, 沈建国. 关于剩余格中滤子的格结构[J]. 数学季刊, 2009, 24(2): 252-257.

ZHANG Xiao-hua, SHEN Jian-guo. On Lattice Structure of Filters in Residuated Lattices [J]. Chinese Quarterly Journal of Mathematics, 2009, 24(2): 252-257.

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