Ideals and congruences in quasi-pseudo-MV algebras

被引：14

作者：

Chen, Wenjuan ^{[1
]}

Dudek, Wieslaw A. ^{[2
]}

机构：

[1] Univ Jinan, Sch Math Sci, 336 West Rd Nan Xinzhuang, Jinan 250022, Shandong, Peoples R China

[2] Wroclaw Univ Technol, Inst Math, Wyb Wyspianskiego 27, PL-50370 Wroclaw, Poland

来源：

SOFT COMPUTING | 2018年 / 22卷 / 12期

基金：

中国国家自然科学基金;

关键词：

Congruences; Ideals; Ideal congruences; Normal ideals; Quasi-pseudo-MV algebras; Weak ideals; NONCOMMUTATIVE GENERALIZATION; VARIETIES; LOGIC;

D O I：

10.1007/s00500-017-2854-6

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Quasi-pseudo-MV algebras (quasi-pMV algebras, for short) were introduced both as the generalization of quasi-MV algebras and as the generalization of pseudo-MV algebras. In the present paper, we mainly investigate ideals and congruences in a quasi-pMV algebra. We present the properties of ideals of quasi-pMV algebras and investigate some special ideals. Furthermore, we study the normal ideals in detail and characterize the bijective correspondence between normal ideals and ideal congruences. Finally, we introduce weak ideals of a quasi-pMV algebra and show the relation existing between normal weak ideals and congruences.

引用

页码：3879 / 3889

页数：11

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