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.

In this paper, we define a new concept of factorization for a bounded bilinear mapping $f:Xtimes Yto Z$, depended on  a natural number $n$ and a cardinal number $kappa$; which is called $n$-factorization property of level $kappa$. Then we study the relation between $n$-factorization property of  level $kappa$ for $X^*$ with respect to $f$ and automatically boundedness and $w^*$-$w^*$-continuity...

Introduction. Let A be a commutative semi-simple Banach algebra and let A(.4) be the set of nonzero multiplicative functionals on A. Denote by A' the strongly closed span of A(^4) and by A" the Banach space adjoint of A'. Modifying a construction of R. Arens [l] we introduce a multiplication in A" under which A" becomes a commutative Banach algebra. A is algebraically isomorphic to a subalgebra...

We prove that all Arens extensions of finite rank Riesz multimorphisms taking values in Archimedean spaces coincide and are multimorphisms. also that, for a class Banach lattices F, which includes F=c0,ℓp,c0(ℓp),ℓp(c0), ℓp(ℓs),1<p,s<∞, among many others, Aron-Berner any F-valued multimorphism between