Ideals and congruences in quasi-pseudo-MV algebras
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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.
KeywordsCongruences Ideals Ideal congruences Normal ideals Quasi-pseudo-MV algebras Weak ideals
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).
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Conflict of interest
Authors declare that they have no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors.
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