剩余格中的滤子

数学季刊 ›› 2006, Vol. 21 ›› Issue (3): 443-447.

剩余格中的滤子

College of Education, Nanyang Institute of Technology, Nanyang 473061, China; Hebi Vocational Technical College, Hebi 458030, China

收稿日期:2005-12-24 出版日期:2006-09-30 发布日期:2023-11-29
作者简介:SHEN Jian-guo(1959-),male,native of Nanyang,Henan,an associate Nanyang Institute of Technology,M.S.D.,engages in non-classical logic algebras.

On Filters of Residuated Lattice

College of Education, Nanyang Institute of Technology, Nanyang 473061, China; Hebi Vocational Technical College, Hebi 458030, China

Received:2005-12-24 Online:2006-09-30 Published:2023-11-29
About author:SHEN Jian-guo(1959-),male,native of Nanyang,Henan,an associate Nanyang Institute of Technology,M.S.D.,engages in non-classical logic algebras.

摘要/Abstract

摘要： This paper is devoted to the discussion of filters in residuated lattices. Some equivalent conditions about filter were given. The structure of generated filter was established. The concept of implicative filter in residuated lattice was proposed with its basic properties being discussed.

关键词: residuated lattice, filter, generated filter, implicative filter

Abstract: This paper is devoted to the discussion of filters in residuated lattices. Some equivalent conditions about filter were given. The structure of generated filter was established. The concept of implicative filter in residuated lattice was proposed with its basic properties being discussed.

Key words: residuated lattice, filter, generated filter, implicative filter

中图分类号:

O153

沈建国, 张晓华. 剩余格中的滤子[J]. 数学季刊, 2006, 21(3): 443-447.

SHEN Jian-guo, ZHANG Xiao-hua . On Filters of Residuated Lattice[J]. Chinese Quarterly Journal of Mathematics, 2006, 21(3): 443-447.

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[6]	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.
[7]	王学芳, 徐扬, 宋振明. 次直既约和不直可分解的格蕴涵代数[J]. 数学季刊, 2004, 19(4): 385-392.
[8]	文成林, 靳丽丽, 周颜芳. 基于单传感器多模型的多分辨目标跟踪融合算法[J]. 数学季刊, 1999, 14(3): 36-42.
[9]	宋振明, 王建平 . Lattice Im plication Homom orphism inIm plication Filter Spaces[J]. 数学季刊, 1998, 13(4): 17-23.
[10]	徐少贤, 黄文平. The Semigroup Characterizations of Positive Implicative BCK-algebras[J]. 数学季刊, 1998, 13(3): 86-90.
[11]	郭天榜, 程伟. Some Properties of Fuzzy Filter and Its Category[J]. 数学季刊, 1998, 13(3): 18-22.
[12]	库热西, Y．B．Jun, 黄文平 . Fuzzy Ordered Filters in Implicative Semigroups[J]. 数学季刊, 1998, 13(2): 53-57.
[13]	田英培, 徐扬. Quasi-uniformitieson Lattice Implication Algebras[J]. 数学季刊, 1998, 13(1): 84-86.
[14]	方捷 . 关于双重MS-代数的滤子[J]. 数学季刊, 1997, 12(1): 30-34.
[15]	刘军 , 徐扬 . On Certain Filters in Lattice Implication Algebras[J]. 数学季刊, 1996, 11(4): 106-110.