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.
Hassani,F . (2016). Algebras defined by homomorphisms. International Journal of Nonlinear Analysis and Applications, 7(2), 153-164. doi: 10.22075/ijnaa.2016.456
MLA
Hassani,F . "Algebras defined by homomorphisms", International Journal of Nonlinear Analysis and Applications, 7, 2, 2016, 153-164. doi: 10.22075/ijnaa.2016.456
HARVARD
Hassani F. (2016). 'Algebras defined by homomorphisms', International Journal of Nonlinear Analysis and Applications, 7(2), pp. 153-164. doi: 10.22075/ijnaa.2016.456
CHICAGO
F Hassani, "Algebras defined by homomorphisms," International Journal of Nonlinear Analysis and Applications, 7 2 (2016): 153-164, doi: 10.22075/ijnaa.2016.456
VANCOUVER
Hassani F. Algebras defined by homomorphisms. IJNAA. 2016;7(2):153-164. doi: 10.22075/ijnaa.2016.456
International Journal of Nonlinear Analysis and Applications