Filters and ideals in the generalization of pseudo-BL algebras

  • Wenjuan ChenEmail author
  • Hongkai Wang


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.


Filters Ideals Pseudo-BL algebras Quasi-pseudo-BL algebras Quasi-pseudo-MV algebras 



This study was funded by the National Natural Science Foundation of China (Grant No. 11501245), China Postdoctoral Science Foundation (No. 2017M622177) and Shandong Province Postdoctoral Innovation Projects of Special Funds (No. 201702005).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of JinanJinanPeople’s Republic of China

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