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Soft Computing

, Volume 22, Issue 12, pp 3879–3889 | Cite as

Ideals and congruences in quasi-pseudo-MV algebras

Foundations

Abstract

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.

Keywords

Congruences Ideals Ideal congruences Normal ideals Quasi-pseudo-MV algebras Weak ideals 

Notes

Acknowledgements

This study was funded by the National Natural Science Foundation of China (Grant No.11501245, 11126301) and Natural Scientific Foundation of Shandong Province (No. ZR2013AQ007).

Compliance with ethical standards

Conflict of interest

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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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of JinanJinanPeople’s Republic of China
  2. 2.Institute of MathematicsWrocław University of TechnologyWrocławPoland

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