It is observed that a CL-algebra (Classical Linear Algebra) contains within it a number of MV-algebras (Many-valued Algebras). A necessary and sufficient condition is obtained when a CL-algebra as a whole reduces to an MV-algebra. All the embedded MValgebras are characterised. A special MV-algebra called the Stem of the CL-algebra is studied to some depth. © 1998 Elsevier Science Inc. All right...

An MV-convergence is a convergence on an MV-algebra which renders the operations continuous. We show that such convergences on a given MV-algebra A are exactly the restrictions of the bounded `-convergences on the abelian `-group in which A appears as the unit interval. Thus the theory of `-convergence and Cauchy structures transfers to MV-algebras. We outline the general theory, and then apply...

The aim of the present paper is to define the localisation of MValgebra of an MV-algebra A with respect to a topology F on A. In the last part of the paper it is proved that the maximal MV-algebra of quotients (defined in [6]) and the MV-algebra of fractions relative to an ∧−closed system (defined in [5]) are MV algebra of localisation. The concept of multiplier for distributive lattices was de...

We prove the following result concerning the inheritance of hyper-duality by block and quotient Bose-Mesner algebras associated with a hyper-dual pair of imprimitive Bose-Mesner algebras. Let M and M̃ denote Bose-Mesner algebras. Suppose there is a hyper-duality ψ from the subconstituent algebra of M with respect to p to the subconstituent algebra of M̃ with respect to p̃. Also suppose thatM is im...

There is given a construction of the entropy of a dynamical system on arbitrary MV-algebra M. If M is the MV-algebra of characteristic functions of a σ-algebra (isomorphic to the σ-algebra), then the construction leads to the Kolmogorov Sinaj entropy. If M is the MV-algebra (tribe) of fuzzy sets, then the construction coincides with the Maličký modification of the Kolmogorov Sinaj entropy for f...

The concept of an MV-algebra was introduced by Chang [4] as an algebraic basis for many-valued logic. It turned out that MV-algebras are a subclass of a more general class of effect algebras [7, 6]. Namely, MV-algebras are in one-to-one correspondence with lattice ordered effect algebras satisfying the Riesz decomposition property [2], the latter are called MV-effect algebras. In the study of c...

Flaminio and Montagna (2008) enlarged the language of MV-algebras by a unary operation σ, called internal state or a state operator, equationally defined so as to preserve the basic properties of a state in its usual meaning. The resulting class of MV-algebras is called state MV-algebras. Jenča (2007) and Vetterlein (2008), using different approaches, represented MV-algebras through the quotien...

In this paper, we define the Smarandache hyper BCC-algebra, and Smarandache hyper BCC-ideals of type 1, 2, 3 and 4. We state and prove some theorems in Smarandache hyper BCC-algebras, and then we determine the relationships between these hyper ideals. © 2011 Elsevier Ltd. All rights reserved.

It is known that any MV -algebra is a topological MV -algebra. For a locally finite MV -algebra A with some algebraic and topological conditions the product A× A becomes a compact Riemann surface (modulo conformal equivalence). Topologically, it is a torus.

An MV-pair is a pair (B, G), where B is a Boolean algebra and G is a subgroup of the automorphism group of B satisfying certain condition. Recently it was proved by one of the authors that for an MV-pair (B, G), ∼G is an effect-algebraic congruence and B/ ∼G is an MV-algebra. Moreover, every MV-algebra M can be represented by an MV-pair in this way. In this paper we show that one can define a s...