Every ℵ1-Σ-CS module is Σ-CS

On (σ, τ)-module extension Banach algebras

Let A be a Banach algebra and X be a Banach A-bimodule. In this paper, we define a new product on $Aoplus X$ and generalize the module extension Banach algebras. We  obtain characterizations of Arens regularity, commutativity, semisimplity, and study the ideal structure and derivations of this new Banach algebra.

Σ _1^1 in Every Real in a Σ _1^1 Class of Reals Is Σ _1^1

We …rst prove a theorem about reals (subsets of N) and classes of reals: If a real X is 1 in every member G of a nonempty 1 1 class K of reals then X is itself 1. We also explore the relationship between this theorem, various basis results in hyperarithmetic theory and omitting types theorems in !-logic. We then prove the analog of our …rst theorem for classes of reals: If a class A of reals is...

on (σ, τ)-module extension banach algebras

let a be a banach algebra and x be a banach a-bimodule. in this paper, we dene a new product on a  x and generalize the module extension banach algebras. we obtain characterizations of arens regularity, commutativity, semisimplity, and study the ideal structure and derivations of this new banach algebra.

σ-Normality of Topological Spaces

*-σ-biderivations on *-rings

Bresar in 1993 proved that each biderivation on a noncommutative prime ring is a multiple of a commutatot. A result of it is a characterization of commuting additive mappings, because each commuting additive map give rise to a biderivation. Then in 1995, he investigated biderivations, generalized biderivations and sigma-biderivations on a prime ring and generalized the results of derivations fo...