In this paper we prove that the category of abelianl-groups is equivalent to the category of perfect MV-algebras. Furthermore, we give a finite equational axiomatization of the variety generated by perfect MV-algebras.

In this paper we prove that the category of abelian l-groups is equivalent to the category of perfect MV-algebras. Furthermore, we give a finite equational axiomatization of the variety generated by perfect MV-algebras.

Representations of monadic MV -algebra, the characterization of locally finite monadic MV -algebras, with axiomatization of them, definability of non-trivial monadic operators on finitely generated free MV -algebras are given. Moreover, it is shown that finitely generated m-relatively complete subalgebra of finitely generated free MV -algebra is projective.

In this paper, inspired by methods of Bigard, Keimel, and Wolfenstein , we develop an approach to sheaf representations of MV-algebras which combines two techniques for the representation of MV-algebras devised by Filipoiu and Georgescu and by Dubuc and Poveda . Following Davey approach , we use a subdirect representation of MV-algebras that is based on local MV-algebras. This allowed us to obtain: a representation of any MV-algebras as MV-algebra of all global sections of a sheaf of local MV-algebras on (...) the spectruum of its prime ideals; a representation of MV-algebras, having the space of minimal prime ideals compact, as MV-algebra of all global sections of a Hausdorff sheaf of MV-chains on the space of minimal prime ideals, which is a Stone space; an adjunction between the category of all MV-algebras and the category of MV-algebraic spaces, where an MV-algebraic space is a pair , where X is a compact topological space and F is a sheaf of MV-algebras with stalks that are local. (shrink)

We look at a hierarchical arrangement of ideals in an MV -algebra. The principal classes of ideals studied are the maximals, the primes, the local and perfect ideals and the semi-locals. Beyond these special classes of ideals are the general ideals. Herein we study some relationships among these classes and, more specifically, the products of ideals of these classes. Among the results obtained are the square of a prime ideal is a local ideal, the finite product of prime ideals is (...) a semilocal ideal. We also show that the set of local ideals shares many of the properties of the class of prime ideals, as the Lying Over Theorem and the Going Up Theorem. (shrink)

Formulas of n variables of Łukasiewicz sentential calculus can be represented, via McNaughton’s theorem, by piecewise linear functions, with integer coefficients, from hypercube [0,1] n to [0,1], called McNaughton functions. As a consequence of the McNaughton representation of a formula it is obtained a canonical form of a formula. Indeed, up to logical equivalence, any formula can be written as an infimum of finite suprema of formulas associated to McNaughton functions which are truncated functions to $[0,1]$ of the restriction to (...) [0,1] n of single hyperplanes, for short, called simple McNaughton functions. In the present paper we will concern with the problem of presenting formulas of Lukasiewicz sentential calculus in normal form. Here we list the main results we obtained: a) we give an axiomatic description of some classes of formulas having the property to be canonically mapped one-to-one onto the class of simple Mc Naughton functions; b) we provide normal forms for Lukasiewicz sentential calculus, making use of formulas defined in a); c) we prove the polynomial complexity of formulas, in normal form, coming from a certain class described as in a); d) we extend the results described in a), b) and c) to Rational Lukasiewicz logic. (shrink)