MARYAM AMYARI - Department of Mathematics, Islamic Azad University, Mshahd, Iran

Let A be a Banach algebra and X be a left A-module and φ:X→A be a module map. Then the operation x.y=φ(x)y (x,y Є X) defines a product on X such that X becomes a Banach algebra denoted by Xφ. We investingate therelationship between the resulting Xφ and the given algebra A.

Banach module, Somple Banach algebra, Banach algebra