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.

let $a$ be a $c^*$-algebra and $e$ be a left hilbert $a$-module. in this paper we define a product on $e$ that making it into a banach algebra and show that under the certain conditions $e$  is arens regular. we also study the relationship between derivations of $a$ and $e$.

In this paper, we study the concept of weakly almost periodic functions on Fréchet algebras. For a algebra [Formula: see text], show that text]. We also text] is Arens regular if and only both are regular. Finally, for sequence algebras prove regualr each

and similarly for the right topological centre Z(r)(A′′). The algebra A is said to be Arens regular if Z(`)(A′′) = Z(r)(A′′) = A′′ and strongly Arens irregular if Z(`)(A′′) = Z(r)(A′′) = A. For example, every C∗-algebra is Arens regular [2]. There has been a great deal of study of these two algebras, especially in the case where A is the group algebra L(G) for a locally compact group G. Results...

Let $A$ be a Banach algebra and $X$ be a Banach $A$-bimodule with the left and right module actions $pi_ell: Atimes Xrightarrow X$ and $pi_r: Xtimes Arightarrow X$, respectively. In this paper, we  study  the topological centers of the left module action $pi_{ell_n}: Atimes X^{(n)}rightarrow X^{(n)}$ and the right module action $pi_{r_n}:X^{(n)}times Arightarrow X^{(n)}$,  which inherit from th...

Let $A$ be a $C^*$-algebra and $E$ be a left Hilbert $A$-module. In this paper we define a product on $E$ that making it into a Banach algebra and show that under the certain conditions $E$  is Arens regular. We also study the relationship between derivations of $A$ and $E$.

A complex algebra A is called ideally factored if Ia = Ca is a left ideal of A for all a ∈ A. In this article, we investigate some interesting properties of ideally factored algebras and show that these algebras are always Arens regular but never amenable. In addition, we investigate ρhomomorphisms and (ρ, τ)-derivations on ideally factored algebra.