In this paper we develop a general representation theory for mv-algebras. We furnish the appropriate categorical background to study this problem. Our guide line is the theory of classifying topoi of coherent extensions of universal algebra theories. Our main result corresponds, in the case of mv-algebras and mv-chains, to the representation of commutative rings with unit as rings of global sec...

Please see [1] for background on MV-algebras. We address the question, which MV-algebras have finite automorphism group. The automorphism group of the free MV-algebra on 1 generator is just the group of order 2 (folklore). In contrast, it is known that the automorphism group of the free MV-algebra on 2 generators is not even locally finite [4, 2]. Not much else seems to be known. Let us restric...

The reticulation of an algebra was first defined for commutative rings by Simmons [19] and it was extended by Belluce to non-commutative rings [3]. As for the algebras of fuzzy logics, Belluce also constructed the reticulation of an MV-algebra [2], G. Georgescu defined the reticulation of a quantale [8] and L. Leuştean made this construction for BL-algebras [13, 14]. In each of the papers cited...

We prove that every MV-effect algebra M is, as an effect algebra, a homomorphic image of its R-generated Boolean algebra. We characterize central elements of M in terms of the constructed homomorphism. 1. Definitions and basic relationships An effect algebra is a partial algebra (E;⊕, 0, 1) with a binary partial operation ⊕ and two nullary operations 0, 1 satisfying the following conditions. (E...

In this paper we propose a semiring-theoretic approach to MV-algebras based on the connection between such algebras and idempotent semirings established in [11] and improved in [4] — such an approach naturally imposing the introduction and study of a suitable corresponding class of semimodules, called MV-semimodules. Besides some basic yet fundamental results of more general interest for semiri...

The ŁΠ-algebras are interesting algebraic structures. They were introduced by Esteva, Godo, and Montagna. These algebras are closely related to the MValgebras and Π-algebras. They have two sets of operations and reduct to one set is an MV-algebra and to the other one is a Π-algebra. Other important reducts of ŁΠ-algebras are so-called PÃ L-algebras (an MV-algebras enriched with product connecti...

We introduce and study a topological structure over vectorial and Riesz MV-algebras, similar to metric spaces. Continuous functions with values in these spaces are studied and a fix point theorem is obtained. Moreover we introduce the concept of derivative and integral of MV-valued functions; i.e. functions with values in a Riesz MV-algebra. Finally we present two applications. 2003 Elsevier In...

We generalize the notion of an MV-algebra in the context of residuated lattices to include noncommutative and unbounded structures. We investigate a number of their properties and prove that they can be obtained from lattice-ordered groups via a truncation construction that generalizes the Chang–Mundici Γ functor. This correspondence extends to a categorical equivalence that generalizes the one...

An algebraic setting for the validity of Pavelka style completeness for some natural expansions of Lukasiewicz logic by new connectives and rational constants is given. This algebraic approach is based on the fact that the standard MV-algebra on the real segment [0, 1] is an injective MV-algebra. In particular the logics associated with MV-algebras with product and with divisible MV-algebras ar...

For any BL-algebra L, we construct an associated lattice ordered Abelian group GL that coincides with the Chang’s `-group of an MV-algebra when the BL-algebra is an MValgebra. We prove that the Chang’s group of the MV-center of any BL-algebra L is a direct summand in GL. We also find a direct description of the complement S(L) of the Chang’s group of the MV-center in terms of the filter of dens...