This paper aims to give a clear and comprehensive view of the relations between the various classes of MV-algebras with product operations. The algebraic hyerarchy, from groups to algebras, can be transported by Γ-functors in order to provide the algebraic semantics for conservative extensions of Łukasiewicz logic. The MV-algebraic tensor product allows us to complete the picture with categoric...

States of unital Abelian lattice-groups (normalised positive group homomorphisms to R) provide an abstraction expected-value operators. A well-known theorem due Mundici asserts that the category (with unit-preserving lattice-group as morphisms) is equivalent algebraic MV-algebras, and their homomorphisms. Through this equivalence, states correspond certain [0,1]-valued functionals on which are ...

In the present paper, by considering the notion of MV-modules which is the structure that naturally correspond to lu-modules over lu-rings, we prove some results on prime A-ideals and state some conditions to obtain a prime A-ideal in MV-modules. Also, we state some conditions that an A-ideal is not prime and investigate conditions that $Ksubseteq bigcup _{i=1}^{n}K_{i}$ implies $Ksubseteq K_{j...

In this paper we make an algebraic study of the variety of M V * –algebras introduced by C. C.Chang as an algebraic counterpart for a logic with positive and negative truth values. We build the algebraic theory of M V * –algebras within its own limits using a concept of ideal and of prime ideal that are very naturally related to the corresponding concepts in –groups. The main results are a subd...

A square root is a unary operation with some special properties. In the paper, we introduce and study roots on EMV-algebras. First, known properties of defined MV-algebras will be generalized for EMV-algebras, also find new ones MV-algebras. We use to characterize Then, relation between an EMV-algebra its representing top element. show that each strict has element, investigate divisible EMV-alg...

The main aim of this talk is twofold. Firstly, to present an elementary method based on Farkas’ lemma for rationals how to embed any finite partial subalgebra of a linearly ordered MV-algebra into Q [0; 1] and then to establish a new elementary proof of the completeness of the Lukasiewicz axioms for which the MV-algebras community has been looking for a long time. Secondly, to present a direct ...

This paper is an attempt at developing a theory of algebraic systems that would correspond in a natural fashion to the N0-valued prepositional calculus^). For want of a better name, we shall call these algebraic systems MV-algebras where MV is supposed to suggest many-valued logics. It is known that the classical two-valued logic gives rise to the study of Boolean algebras and, as can be expect...

MV-algebras were introduced by Chang as an algebraic counterpart of the Lukasiewicz infinite-valued logic. D. Mundici proved that the category of MV-algebras is equivalent to the category of abelian l-groups with strong unit. A. Di Nola and A. Lettieri established a categorical equivalence between the category of perfect MV-algebras and the category of abelian l-groups. In this paper we investi...

In his classical paper 1 , Chang invented the notion of MV-algebra in order to provide an algebraic proof of the completeness theorem of infinite valued Lukasiewicz propositional calculus. Recently, the algebraic theory of MV-algebras is intensively studied, see 2–5 . The notion of derivation, introduced from the analytic theory, is helpful to the research of structure and property in algebraic...