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Ideals and congruences in quasi-pseudo-MV algebras

Research paper by Wenjuan Chen, Wieslaw A. Dudek

Indexed on: 26 Oct '17Published on: 03 Oct '17Published in: Soft Computing



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.