A non-commutative generalization of quasi-MV algebras

In this paper, we introduce and investigate a non-commutative generalization of quasi-MV algebras, called pseudo-quasi-MV algebras (pseudo-qMV algebras for short). And then we characterize the bijective relation between ideal congruences and normal ideals of a pseudo-qMV algebra. Finally, we prove that pseudo-qMV algebras are categorically equivalent to pseudo-quasi-Wajsberg algebras which are the non-commutative generalization of quasi-Wajsberg algebras.