In the present paper we define the (pseudo) MV-algebras with n-ary operators, generalizing MV-modules and product MV-algebras. Our main results assert that there are bijective correspondences between the operators defined on a pseudo MV-algebra and the operators defined on the corresponding `-group. We also provide a categorical framework and we prove the analogue of Mundici’s categorical equiv...

Fuzzy ideals of pseudo MV-algebras are investigated. The homomorphic properties of fuzzy prime ideals are given. A one-to-one correspondence between the set of maximal ideals and the set of fuzzy maximal ideals μ satisfying μ(0) = 1 and μ(1) = 0 is obtained.

In this paper, we investigate the relationships between lattice-groups and two types of pseudo MV-algebras. Moreover, we find pseudo MValgebras induced by functions. We give their examples. Mathematics Subject Classification: 06D35, 06D50, 06F05, 06F15

The paper provides a study of pseudo MV-algebras with square roots. We introduce different notions root on MV-algebra, and present their main properties. show that the class pseudo-MV-algebras roots is proper subvariety variety MV-algebras. Then, we define strict to classify found relationship between strongly atomless Finally, investigate representable symmetric MV-algebras, complete character...

Pseudo-BCK algebras were introduced by G. Georgescu and A. Iorgulescu as a generalization of BCK algebras in order to give a corresponding structure to pseudo-MV algebras, since the bounded commutative BCK algebras corresponde to MV algebras. Properties of pseudo-BCK algebras and their connections with other fuzzy structures were established by A. Iorgulescu and J. Kühr. The aim of this paper i...

The notion of a state is an analogue of a probability measure and was first introduced by Kôpka and Chovanec for MV-algebras and by Riec̆an for BLalgebras. The states have also been studied for different types of non-commutative fuzzy structures such as pseudo-MV algebras, pseudo-BL algebras, bounded R`monoids, residuated lattices and pseudo-BCK semilattices. In this paper we investigate the sta...

The natural bijective correspondence between MV-algebras and pseudorings is generalized to the case of pseudoMV-algebras. We first introduce the concepts of noncommutative pseudorings and strong pseudo De Morgan algebras. Then, we show that they both correspond to pseudo MV-algebras via symmetric difference in a natural bijective way.