University of Guilan Journal of Algebra and Related Topics 2345-3931 1 1 2013 11 01 Arens regularity and derivations of Hilbert modules with the certain product 31 39 43 EN A. Sahleh University of Guilan L. Najarpisheh University of Guilan Journal Article 2013 07 31 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 $E$. https://jart.guilan.ac.ir/article_43_c935ff4a35e1d9bcd1ab677e11c33519.pdf