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...

We consider a non-associative generalization of MV-algebras. The underlying posets of our non-associative MV-algebras are not lattices, but they are related to so-called λ-lattices. c ©2007 Mathematical Institute Slovak Academy of Sciences 1. Non-associative MV-algebras As known, MV-algebras were introduced in the late-fifties by C . C . C h a n g as an algebraic semantics of the Lukasiewicz ma...

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...

This paper presents an algebraic approach of some many-valued generalizations of modal logic. The starting point is the de nition of the [0, 1]-valued Kripke models, where [0, 1] denotes the well known MV-algebra. Two types of structures are used to de ne validity of formulas: the class of frames and the class of Šn-valued frames. The latter structures are frames in which we specify in each wor...

The unit interval in a partially ordered abelian group with order unit forms an interval effect algebra (IEA) and can be regarded as an algebraic model for the semantics of a formal deductive logic. There is a categorical equivalence between the category of IEA’s and the category of unigroups. In this article, we study the IEA-unigroup connection, focusing on the cases in which the IEA is a Boo...