In this paper, by considering the notion of upsets we construct some topologies on BLalgebras. We show that any BL-algebras with respect to these topologies formes semitopological BLalgebra. Then we obtain some of the topological aspects of theses structures such as connectivity and compactness. Moreover, we introduced two kinds of semitopological MV -algebra by using two kinds of definition of...

We define the Lukasiewicz Transform as a residuated map and a homomorphism between semimodules over the semiring reducts of an MV-algebra. Then we describe the “ Lukasiewicz Transform Based” ( LTB) algorithm for image processing. We also propose a strong extension of such concepts and results in the framework of quantales and quantale modules. 1 The Lukasiewicz transform and its applications Th...

In this paper, we investigate related properties of some particular derivations and give some characterizations of additive derivations in MV-algebras. Then, we obtain that the fixed point set of additive derivations is still an MV-algebra. Also, we study Boolean additive derivations and their adjoint derivations. In particular, we get that the fixed point set of Boolean addition derivations an...

Definition 1. An algebra (A,⊕,∗ , 0) with a binary operation ⊕ : A×A → A and with a unary operation ∗ : A → A and a constant 0, is said to be an MV -algebra iff satisfies the following conditions for all a, b, c ∈ A: (1) (A,⊕, 0) is a commutative monoid; (2) x⊕ 0∗ = 0∗ for every x ∈ A; (3) (x∗)∗ = x for every x ∈ A; (4) (x∗ ⊕ y)∗ ⊕ y = (x⊕ y∗)∗ ⊕ x for every x, y ∈ A. ¿From (4), setting y = 0∗,...

This paper provides a review on major ergodic features of semiindependent hyper MV –algebra dynamical systems. Theorems are presented to make contribution to calculate the entropy. Particularly, it is proved that the total entropy of those semi-independent hyper MV –algebra dynamical systems that have a generator can be calculated with respect to their generator rather than considering all the ...

Following the study of sharp domination in effect algebras, in particular, in atomic Archimedean MV-effect algebras it is proved that if an atomic MV-effect algebra is uniformly Archimedean then it is sharply dominating.

Let Gr be the affine Grassmannian for a connected complex reductive group G. Let CG be the complex vector space spanned by (equivalence classes of) Mirković-Vilonen cycles in Gr. The Beilinson-Drinfeld Grassmannian can be used to define a convolution product on MV-cycles, making CG into a commutative algebra. We show, in type A, that CG is isomorphic to C[N], the algebra of functions on the uni...