Residue class rings of Z/Ring homomorphism/Fact

Let ${}d\geq 0$ be a natural number.

Then there exists a uniquely determined ring structure on ${}\mathbb {Z} /(d)$ such that the

residue class mapping

$\mathbb {Z} \longrightarrow \mathbb {Z} /(d),a\longmapsto {\overline {a}}\,,$

is a

ring homomorphism.

${}\mathbb {Z} /(d)$ is a commutative ring with ${}d$ elements (for ${}d\geq 1$).

Write a proof