‎In this paper‎, ‎we introduce the notion of the radical of a $PMV$-algebra $A$ and we charactrize radical $A$ via elements of $A$‎. ‎Also‎, ‎we introduce the notion of the radical of a $cdot$-ideal in $PMV$-algebras‎. ‎Several characterizations of this radical is given‎. ‎We define the notion of a semimaximal $cdot$-ideal in a $PMV$-algebra‎. ‎Finally we show that $A/I$ has no nilpotent elemen...

In this paper I give an explicit conformal field theory description of (2+1)dimensional BTZ black hole entropy. In the boundary Liouville field theory I investigate the reducible Verma modules in the elliptic sector, which correspond to certain irreducible representations of the quantum algebra Uq(sl2)⊙Uq̂(sl2). I show that there are states that decouple from these reducible Verma modules in a s...

The notions of a S fuzzy ∧ sub semi lattice, a S fuzzy ideal and a S fuzzy prime ideal of a bounded lattice with truth values in a bounded ∧ sub semi lattice S are introduced which generalize the existing notions with truth values in a unit interval of real numbers. Finally, S fuzzy prime ideal theorem is proved. 2010 AMS Classification: 03G10, 46H10, 06D50, 08A72

Let R be a unital semi-simple commutative complex Banach algebra, and let M(R) denote its maximal ideal space, equipped with the Gelfand topology. Sufficient topological conditions are given on M(R) for R to be a projective free ring, that is, a ring in which every finitely generated projective R-module is free. Several examples are included, notably the Hardy algebra H∞(X) of bounded holomorph...

In this paper we will present class of new lower bounds for the Quadratic Semi-Assignment Problem (QSAP). These bounds are based on recent results about polynomially solvable cases, in particular we will consider the QSAP's whose quadratic cost coefficients define a reducible graph. Several lower bounds will be computationally compared, moreover we will present a method which improves these bou...

We assign two parameters to an M-ideal J in a Ba-nach space X, called the lower and upper grade, which are deened in terms of the size of balls contained in the set of best approximants from J. These quantities serve to measure how far J resembles an M-summand, and they enter into geometric descriptions in various ways. For instance they allow estimates of the interior of the metric complement ...

Abstract. Let L and M be two finite lattices. The ideal J(L,M) is a monomial ideal in a specific polynomial ring and whose minimal monomial generators correspond to lattice homomorphisms ϕ: L→M. This ideal is called the ideal of lattice homomorphism. In this paper, we study J(L,M) in the case that L is the product of two lattices L_1 and L_2 and M is the chain [2]. We first characterize the set...