\b[$\mathbb Z/4\mathbb Z$ is a <ring> but not a <field>.] Quotient operations inherit associativity and distributivity from the integers, and residues have <additive inverses>. However the nonzero residue $\overline2$ satisfies $\overline2\,\overline2=\overline0$, so it cannot be invertible. A <field> has no nonzero <zero divisors>.

Solution

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

 Solution (source code)