Fields

In the setting of Class Theory NBG: the Axioms, Standing Conventions and Basic Notation, let $r$ be a set with binary operations $+$ and $\cdot$ and elements $0,1\in r$.

¶ $r$, with $+$, $\cdot$, $0$ and $1$, is a field if it is a commutative ring, $0\neq1$, and every $x\in r$ with $x\neq0$ has some $y\in r$ with $x\cdot y=1$.