ILI-ideals and prime LI-ideals in lattice implication algebras

被引：38
作者：
Liu, YL [1 ]
Liu, SY
Xu, Y
Qin, KY
机构：
[1] Nanping Teachers Coll, Dept Math, Fujian 353000, Peoples R China
[2] SW Jiaotong Univ, Dept Appl Math, Chengdu 610031, Sichuan, Peoples R China
[3] Xidian Univ, Dept Appl Math, Xian 710071, Peoples R China
来源：
INFORMATION SCIENCES | 2003年 / 155卷 / 1-2期
基金：
中国国家自然科学基金;
关键词：
lattice implication algebra; ILI-ideal; prime LI-ideal; maximal LI-ideal;
D O I：
10.1016/S0020-0255(03)00159-2
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
The notions of ILI-ideals and maximal LI-ideals of lattice implication algebras are introduced, respectively. The properties of ILI-ideals, prime LI-ideals and maximal LI-ideals are investigated. Several characterizations of ILI-ideals and prime LI-ideals are given. The extension theorem of ILI-ideals is obtained. The relations between ILI-ideals and LI-ideals, between ILI-ideals and implication filter, between prime LI-ideals and maximal LI-ideals, between prime LI-ideals and ILI-ideals, between maximal LI-ideals and ILI-ideals, between maximal LI-ideals and LI-ideals, and between prime LI-ideals and LI-ideals are investigated, respectively. Some classes of lattice implication algebras are characterized by their ILI-ideals (respectively prime LI-ideals, maximal LI-ideals). (C) 2003 Elsevier Inc. All rights reserved.
引用
收藏
页码：157 / 175
页数：19
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