# Math Help - Subring of the complex

1. ## Subring of the complex

Let A the subring of the complex $A=\{ a + b \sqrt{2}: a,b \in \mathbb{Z}\}$

a) Prove that $A$ is a $\mathbb{Z}$-module and an $A$-module, with the product as action

b) Prove that the function $a + b \sqrt{2} \rightarrow a+b$ is a homomorphism of $\mathbb{Z}$-modules from $A$ to $A$ but isn´t a homomorphism of $A$-modules

c) Prove that, as $\mathbb{Z}$-module, A is isomorphic to $\mathbb{Z} \oplus \mathbb{Z}$

thanks!!