Document Type : Research Paper

Author

• Feysal Hassani

Payame Noor University

Abstract

Let $\mathcal{R}$ be a  commutative ring with identity, let $A$ and $B$ be two $\mathcal{R}$-algebras and $\phi :B⟶A$ be an $\mathcal{R}$-additive algebra homomorphism. We introduce a new algebra $A{\times }_{\phi }B$, and give some basic properties of this algebra. Generalized $2$-cocycle derivations on $A{\times }_{\phi }B$ are studied. Accordingly, $A{\times }_{\phi }B$ is considered from the perspective of Banach algebras.

Keywords

• algebra
• cocycle
• generalized derivation
• Banach algebra