The tensor virial theorem for subsystems is formulated for threecomponent systems and further effort is devoted to a special case where the inner subsystems and the central region of the outer one are homogeneous, the last surrounded by an isothermal homeoid. The virial equations are explicitly written under the additional restrictions: (i) similar and similarly placed inner subsystems, and (ii...

A pseudo-addition in BL-algebras is a binary operation that is associative and non commutative. The aim of this paper is to use the notion of pseudo-addition to study the notion of ideal and fuzzy ideal as a natural generalization of that of ideal and fuzzy ideal in MV-algebras. Using a pseudo-addition, we characterize fuzzy ideals and also obtain a concrete description of the fuzzy ideals gene...

Abstract. A few things are known, and many are unknown, on the automorphism group of the free MV-algebra over n − 1 generators. In this paper we show that this group appears as the stabilizer of 1l in the larger group of all automorphisms of the free cancellative hoop over n generators. Both groups have a dual action on the same space, namely the (n − 1)-dimensional cube. The larger group has a...

In this paper, we introduce the notion of bi-Smarandache BL-algebra, bi-weak Smarandache BL-algebra, bi-Q-Smarandache ideal and bi-Q-Smarandache implicative filter, we obtain some related results and construct quotient of bi-Smarandache BL-algebras via MV-algebras (or briefly bi-Smarandache quotient BL-algebra) and prove some theorems. Finally, the notion of bi-strong Smarandache BL-algebra is ...

We represent every normal-valued GMV-algebra as a GMV-algebra of real-valued functions; we also describe the universal MV-algebras and universal normal-valued GMV-algebras with a prescribed set of components.

We investigate an expansion of quasi-MV algebras ([10]) by a genuine quantum unary operator. The variety p 0QMV of such p 0 quasi-MV algebras has a subquasivariety whose members called cartesian can be obtained in an appropriate way out of MV algebras. After showing that cartesian p 0 quasi-MV algebras generate p 0QMV, we prove a standard completeness theorem for p 0QMV w.r.t. an algebra over t...

A set E equipped with a partial, commutative and associative operation ⊕, containing elements 0 and 1, in which the existence of a unique inverse element x′ to any x ∈ E is guaranteed, and a⊕ 1 is admitted only if a = 0 is well known as effect algebra. Effect algebras were introduced by Foulis and Bennet [3] and simultaneously by Kôpka and Chovanec [7] as D-posets. An effect algebra equipped wi...

The framework. In 1956, G. Birkhoff G. and R.S. Pierce [1] conjectured the following: do the algebra of piecewise polynomial functions with real coefficients and the algebra of functions that can be written as Inf and Sup of finitely many polynomials coincide? The conjecture – that can be equivalently stated asking for the free n-generated lattice-ordered algebra to be isomorphic with the algeb...

MV-algebras were introduced by Chang in 1958 preliminary to his providing an algebraic completeness proof for the K0-vaΓued Lukasiewicz propositional logic, LXo. In this paper a method is given for determining, for an arbitrary normal extension of LKo, an MV-algebra characteristic for the extension. The characteristic algebras are finite direct products of two sets of linearly ordered MV-algebr...