Lawrence Peter Belluce

The Prime Spectrum of an MV‐Algebra

In this paper we show that the prime ideal space of an MV-algebra is the disjoint union of prime ideal spaces of suitable local MV-algebras. Some special classes of algebras are defined and their spaces are investigated. The space of minimal prime ideals is studied as well. Mathematics Subject Classification: 03B50, 06D99.

Commutative rings whose ideals form an MV‐algebra

In this work we introduce a class of commutative rings whose defining condition is that its lattice of ideals, augmented with the ideal product, the semi-ring of ideals, is isomorphic to an MV-algebra. This class of rings coincides with the class of commutative rings which are direct sums of local Artinian chain rings with unit (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Yosida Type Representation for Perfect MV-Algebras

In [9] Mundici introduced a categorical equivalence Γ between the category of MV-algebras and the category of abelian -groups with strong unit. Using Mundicis functor Γ, in [8] the authors established an equivalence between the category of perfect MV-algebras and the category of abelian -groups. Aim of the present paper is to use the above functors to provide Yosida like representations (see [4]) of a large class of MV-algebras. Mathematics Subject Classification: 03G20, 03B50, 06D30, 06F20.

MV-semirings and their Sheaf Representations

In this paper we show that the classes of MV-algebras and MV-semirings are isomorphic as categories. This approach allows one to keep the inspiration and use new tools from semiring theory to analyze the class of MV-algebras. We present a representation of MV-semirings by MV-semirings of continuous sections in a sheaf of commutative semirings whose stalks are localizations of MV-semirings over prime ideals. Using the categorical equivalence, we obtain a representation of MV-algebras.

Perfect MV-algebras and their Logic

In this paper, after recounting the basic properties of perfect MV-algebras, we explore the role of such algebras in localization issues. Further, we analyze some logics that are based on Łukasiewicz connectives and are complete with respect to linearly ordered perfect MV-algebras.

Abelian ℓ-Groups with Strong Unit and Perfect MV-Algebras

We investigate the class of abelian ℓ-groups with strong unit corresponding to perfect MV-algebras via the Γ functor, showing that this is a universal subclass of the class of all abelian ℓ-groups with strong unit and describing the formulas that axiomatize it. We further describe results for classes of abelian ℓ-groups with strong unit corresponding to local MV-algebras with finite rank.

Perfect MV-Algebras and l-Rings

ABSTRACT In this paper we shall prove that l-rings are categorally equivalent to the MV*-algebras, a subcategory of perfect MV-algebras. We shall use this equivalence in order to characterize l-rings as quotients of certain semirings of matrices over MV*-algebras. We shall establish a relation between l-ideals in l-rings and some ideals in MV*-algebras. This edlows us to study the MV* f-algebras, a subclass of the MV*-algebras corresponding to the f-rings.

SUB ALGEBRAS, DIRECT PRODUCTS AND ASSOCIATED LATTICES OF MV-ALGEBRAS

MV-algebras were introduced by C. C. Chang [3] in 1958 in order to provide an algebraic proof for the completeness theorem of the Lukasiewicz infinite valued propositional logic. In recent years the scope of applications of MV-algebras has been extended to lattice-ordered abelian groups, AF C * -algebras [10] and fuzzy set theory [1].

Algebraic geometry for mv-algebras

In this paper we try to apply universal algebraic geometry to MV algebras, that is, we study “MV algebraic sets” given by zeros of MV polynomials, and their “coordinate MV algebras”. We also relate algebraic and geometric objects with theories and models taken in Łukasiewicz many valued logic with constants. In particular we focus on the structure of MV polynomials and MV polynomial functions on a given MV algebra.

On generalizing the Nullstellensatz for MV algebras

In this article, first we generalize from the MV algebra [0,1] to an arbitrary MV algebra A the well-known Galois connection (V ,I) between the powerset of each power of [0,1] and the powerset of the corresponding free MV algebra. Then, in analogy with the Nullstellensatz of classical algebraic geometry, we study the closure operators obtained by composing the