Residuated lattices and lattice effect algebras

被引：9

作者：

Zhou, Xiang-Nan

Li, Qing-Guo ^{[1
]}

Wang, Guo-Jun

机构：

[1] Hunan Univ, Dept Appl Math, Changsha 410082, Peoples R China

[2] Shaanxi Normal Univ, Inst Math, Xian 710062, Peoples R China

[3] Xian Jiaotong Univ, Ctr Sci Res, Xian 710049, Peoples R China

来源：

FUZZY SETS AND SYSTEMS | 2007年 / 158卷 / 08期

基金：

美国国家科学基金会;

关键词：

lattice effect algebra; partial operation; residuated lattice; involutive residuated lattice;

D O I：

10.1016/j.fss.2006.12.014

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Residuated lattices and lattice effect algebras arose in two rather different fields. In this paper, by introducing two partial operations in effect algebras, we investigate the mutual relationship between involutive residuated lattices and lattice effect algebras. We prove that a lattice effect algebra under certain conditions can be extended to an involutive residuated lattice and the latter with certain properties can be restricted to the former. Especially, an sufficient and necessary condition for an involutive residuated lattice to be a lattice effect algebra with the Riesz decomposition property is obtained. (c) 2007 Elsevier B.V. All rights reserved.

引用

页码：904 / 914

页数：11

共 23 条

[1] Phi-symmetric effect algebras [J].