Why is this a ring homomorphism?
$$\phi:R\to R/I$$ where $I$ is an ideal, given by $\phi:r\mapsto r+I$.
To be a ring homomorphism it needs to be a homomorphism of addition and multiplication, i.e:
where $a,b\in R$
Here we have:
1) $\phi(ab)=ab+I$ and $\phi(a)\phi(b)=ab+aI+bI+I^2=ab+I^2$ and I imagine then that $I^2=I$?
2) $\phi(a+b)=a+b+I$ and $\phi(a)+\phi(b)=a+b+2I=a+b+I$.
So this holds I suppose if $I^2=I$, does this just come because $aI=I$ and let $a=I$ and then $II=I$?