02 - First Isomorphism Theorem

First Isomorphism Theorem

Kernel $\mathrm{Ker}(\varphi ):={\varphi }^{-1}(0)$ of a ring homomorphism $\varphi :R\to S$ is an ideal

Image $\mathrm{Im}(\varphi )$ is a subring of $S$, and $\varphi$ induces an isomorphisms of rings

$$R\setminus \mathrm{Ker}(\varphi )\cong \mathrm{Im}(\varphi )$$

Proof (Missing)

Exercise (TODO?)