Show that the group of rational numbers $\Bbb Q$ doesn't contain non-trivial subgroups $G$ and $H$ such that $\Bbb Q$ is isomorphic to $G \oplus H$
Let $R$ be $\Bbb Z_2[x]/\langle x^2 + 1 \rangle$. Prove that $R$ is not isomorphic to $\Bbb Z_4$.
I think I need some help in doing not isomorphism. How to prove that stuff?