Algebras defined by homomorphisms

Document Type : Research Paper


Payame Noor University


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


Volume 7, Issue 2 - Serial Number 2
December 2016
Pages 153-164
  • Receive Date: 15 September 2016
  • Revise Date: 04 October 2016
  • Accept Date: 19 October 2016