Past exam of the algebra, analysis and differential equations 1 course of the University of Oxford / 2004 / Algebra / 3 / iii / Solution

$\mathbb{Z}/3\mathbb{Z}$ is a field, and consequently also a ring. Its nonzero elements are $\overline{1}$ and $\overline{2}$, with inverses $\overline{1}$ and $\overline{2}$ respectively. The quotient ring axioms are inherited as in the preceding part.