Lattice implication ordered semigroups

被引：21
|
作者：
Pan, Xiaodong [1 ,2 ]
Xu, Yang [2 ]
机构：
[1] SW Jiaotong Univ, Dept Math, Chengdu 610031, Peoples R China
[2] SW Jiaotong Univ, Intelligent Control Dev Ctr, Chengdu 610031, Peoples R China
来源：
INFORMATION SCIENCES | 2008年 / 178卷 / 02期
基金：
中国国家自然科学基金; 高等学校博士学科点专项科研基金;
关键词：
lattice ordered semigroup; implication semigroup; lattice implication algebra; filter; sl ideal;
D O I：
10.1016/j.ins.2007.08.017
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
From the viewpoint of semantics, lattice implication algebras provide a basis to establish lattice-valued logic with truth value in a relatively general lattice. In this paper, we first introduce two notions of lattice implication n-ordered semigroup, and lattice implication p-ordered semigroup, which induced by lattice implication algebras. Secondly, we study some of their basic properties and prove that a lattice implication n-ordered semigroup is a residuated semigroup, and a lattice implication p-ordered semigroup is an arithmetic lattice ordered semigroup. We also define the homomorphism mapping between lattice implication n-ordered semigroups. Finally, we discuss some properties of filters and sl ideals in lattice implication n-ordered semigroups and lattice implication p-ordered semigroups. (c) 2007 Elsevier Inc. All rights reserved.
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页码：403 / 413
页数：11
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