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Some classes of quasi-pseudo-MV algebras

The focus of this article is to classify quasi-pseudo-MV algebras (quasi-pMV algebras, for short) based on the properties of operations and ideals in quasi-pMV algebras. According to the operations, quasi-pMV algebras are divided into two classes, one is based on the commutativity of the binary operation and the other is based on the consistency of the two unary operations. For these classes, we mainly characterize under what conditions quasi-pMV algebras are commutative and study pseudo-quasi-MV algebras. According to the properties of ideals, we investigate and classify local quasi-pMV algebras.