I was reading some notes on Ring theory that I found online and it says this :
If $R$ is any ring and $S ⊂ R$ is a subring, then the inclusion $i: S → R$ is a ring homomorphism.
I don't know what is meant by "inclusion $i: S → R$". Can someone elaborate on this?
The inclusion of $S$ into $R$ is the function $i : S \to R$ given by $i(s) = s$, as $S$ is just a subset of $R$. The fact this is a ring homomorphism is clear. Why do we even want to talk about such a seemingly non-interesting map? Well if you have another ring homomorphism $\phi : R \to A$ then you can form the restriction of this map to $S$ just by precomposing with $i$, so we have $\phi \circ i:S \to A$.