次直既约和不直可分解的格蕴涵代数

数学季刊 ›› 2004, Vol. 19 ›› Issue (4): 385-392.

次直既约和不直可分解的格蕴涵代数

1.Department of Mathematics, Ocean University of China, Qingdao 266003, China; 2.Department of Applied Mathematics, Southwest Jiaotong University, Chengdu 610031, China

收稿日期:2002-12-26 出版日期:2004-12-30 发布日期:2024-03-05
作者简介:WANG Xue-fang(1975-),female,native of Linyi,Shandong,Ph.D.,engages in fuzzy logic and intelligent control.
基金资助:
SupportedbytheNationalNaturalScienceFoundationofChina(60074014)；

Subdirectly Irreducible and Directly Indecomposable Lattice Implication Algebras

1.Department of Mathematics, Ocean University of China, Qingdao 266003, China; 2.Department of Applied Mathematics, Southwest Jiaotong University, Chengdu 610031, China

Received:2002-12-26 Online:2004-12-30 Published:2024-03-05
About author:WANG Xue-fang(1975-),female,native of Linyi,Shandong,Ph.D.,engages in fuzzy logic and intelligent control.
Supported by:
SupportedbytheNationalNaturalScienceFoundationofChina(60074014)；

摘要/Abstract

摘要： Lattice implication algebra is an algebraic structure that is established by combining lattice and implicative algebra. It originated from the study on lattice-valued logic. In this paper, we characterize two special classes of lattice implication algebra, namely, subdi-rectly irreducible and directly indecomposable lattice implication algebras. Some important results are obtained.

关键词: many-valued logic, lattice implication algebra, flter, ultra-filter, prime flter

Abstract: Lattice implication algebra is an algebraic structure that is established by combining lattice and implicative algebra. It originated from the study on lattice-valued logic. In this paper, we characterize two special classes of lattice implication algebra, namely, subdi-rectly irreducible and directly indecomposable lattice implication algebras. Some important results are obtained.

Key words: many-valued logic, lattice implication algebra, flter, ultra-filter, prime flter

中图分类号:

O153.5

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.

WANG Xue-fang, XU Yang, SONG Zhen-ming. Subdirectly Irreducible and Directly Indecomposable Lattice Implication Algebras[J]. Chinese Quarterly Journal of Mathematics, 2004, 19(4): 385-392.

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