Cubical sets have a directed homology, studied in a previous paper and consisting of preordered abelian groups, with a positive cone generated by the structural cubes. By this additional information, cubical sets can provide a sort of ‘noncommutative topology’, agreeing with some results of noncommutative geometry but lacking the metric aspects of C∗-algebras. Here, we make such similarity stri...

In this paper, we first present the new concept of $2$-normed algebra. We investigate the structure of this algebra and give some examples. Then we apply a fixed point theorem to prove the stability and hyperstability of $(alpha, beta, gamma)$-derivations in $2$-Banach algebras.

Some inequalities in normed algebras that provides lower and upper bounds for the norm of ∑n j=1 ajxj are obtained. Applications for estimating the quantities ∥∥∥∥x−1∥∥x± ∥∥y−1∥∥ y∥∥ and ∥∥∥∥y−1∥∥x± ∥∥x−1∥∥ y∥∥ for invertible elements x, y in unital normed algebras are also given.

almost multiplier is rather a new concept in the theory of almost functions. in thispaper we discuss on the boundedness of almost multipliers on some special banach algebras,namely stable algebras. we also dene an adjoint and extension for almost multiplier.

Every finite dimensional normed algebra is isomorphic to the direct product of or , it also proved these algebras are ultrasemiprime algebras. In this paper, proof and generalized any

(Minor corrections and additions have been made. The page layout has also been changed.) 0 Contents Contents 1 Abstract 2 Chapter 1: Constructions and Elementary Properties and Applications of Algebraic Extensions of Normed Algebras 3

Metric algebras are metric variants of Σ-algebras. They are first introduced in the field of universal algebra to deal with algebras equipped with metric structures such as normed vector spaces. Recently a similar notion of quantitative algebra is used in computer science to formulate computational effects of probabilistic programs. In this paper we show that varieties of metric algebras (class...

We describe the role of algebraic extensions in the theory of commutative, unital normed algebras, with special attention to uniform algebras. We shall also compare these constructions and show how they are related to each other. [MSC: 46J05, 46J10]