Filters and ideals in the generalization of pseudo-BL algebras

被引：0
作者：
Wenjuan Chen
Hongkai Wang
机构：
[1] University of Jinan,School of Mathematical Sciences
来源：
Soft Computing | 2020年 / 24卷
关键词：
Filters; Ideals; Pseudo-BL algebras; Quasi-pseudo-BL algebras; Quasi-pseudo-MV algebras;
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学科分类号：
摘要：
In this paper, we introduce the notion of quasi-pseudo-BL algebras as the generalization of pseudo-BL algebras and quasi-pseudo-MV algebras. First, we investigate the properties of quasi-pseudo-BL algebras and show the subdirect product composition of any quasi-pseudo-BL algebra. Especially, some properties of good quasi-pseudo-BL algebras are presented. Second, we discuss the filters of quasi-pseudo-BL algebras and prove that there exists a bijective correspondence between normal filters and filter congruences on a quasi-pseudo-BL algebra. The properties of some special filters are also discussed. Finally, we study the ideals of quasi-pseudo-BL algebras and investigate some connections between ideals and filters of a quasi-pseudo-BL algebra.
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页码：795 / 812
页数：17
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