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...

In last ten years many mathematicians have studied properties of BL-algebras endowed with a topology. For example A. Di Nola and L. Leustean cite{dn} studied compact representations of BL-algebras, L. C. Ciungu cite{ciu} investigated some concepts of convergence in the class of perfect BL-algebras, J. Mi Ko and Y. C. Kim cite{jun} studied relationships between closure operators and BL-algebras,...

We develop a mechanism for classication of isomorphism types of non-trivial semisimple Hopf algebras whose group of grouplikes G(H) is abelian of prime index p which is the smallest prime divisor of |G(H)|. We describe structure of the second cohomology group of extensions of kCp by k G where Cp is a cyclic group of order p and G a finite abelian group. We carry out an explicit classification f...

We give topological proofs of Görnemann’s adaptation to Heyting algebras of the Rasiowa-Sikorski Lemma for Boolean algebras; and of the Rauszer-Sabalski generalisation of it to distributive lattices. The arguments use the Priestley topology on the set of prime filters, and the Baire category theorem. This is preceded by a discussion of criteria for compactness of various spaces of subsets of a ...

The aim of this paper is to introduce the notion of anti fuzzy (prime) deductive system in BL-algebra and to investigate their properties. It is shown that the set of all deductive systems (with the empty set) of a BL-algebra X is equipotent to a quotient of the set of all anti fuzzy deductive systems of X. The anti fuzzy prime deductive system theorem of BL-algebras is also proved. Anti Fuzzy ...

In this paper, by using the sequence of adjointable operators from pro-C*-algebra $ mathcal{A} $ into a Hilbert $ mathcal{A} $-module $ E $. We introduce frames with bounds in pro-C*-algebra $ mathcal{A} $. New frames in Hilbert modules over pro-C*-algebras are called standard $ ast $-frames of multipliers. Meanwhile, we study several useful properties of standard $ ast $-frames in Hilbert modu...

We consider algebras over a field K defined by a presentation K〈x1, . . . , xn : R〉, where R consists of ( n 2 ) square-free relations of the form xixj = xkxl with every monomial xixj , i 6= j, appearing in one of the relations. Certain sufficient conditions for the algebra to be noetherian and PI are determined. For this, we prove more generally that right noetherian algebras of finite Gelfand...

In this paper we prove that the noncyclic generic abelian crossed product p-algebras constructed by Amitsur and Saltman in [AS78] remain noncyclic after tensoring by any prime to p extension of their centers. We also prove that an example due to Saltman of an indecomposable generic abelian crossed product with exponent p and degree p 2 remains indecomposable after any prime to p extension. 0 In...

Temperley-Lieb algebras have been generalized to sl(3, C) web spaces. Since a cubic bipartite planar graph with suitable directions on edges is a web, the quantum sl(3) invariants naturally extend to all cubic bipartite planar graphs. First we completely classify them as a connected sum of primes webs. We also provide a method to find all prime webs and exhibit all prime webs up to 20 vertices....

In this document we consider the prime spectrum of an MV-algebra with certain natural operations. These are used to show connections between the classes of prime lattice filters and prime implication filters.