Solution
= Solution
A <ring> is a set with an abelian-group <addition>, associative <multiplication> and both distributive laws; here we use <rings> with multiplicative identity. A <field> is a nonzero <commutative ring> in which every nonzero element has a multiplicative inverse.
\b[The <positive integers> form neither a <ring> nor a <field>.] They do not contain an <additive identity> zero, and they also lack <additive inverses>.