Field axioms
Axioms defining a field as a commutative unital ring in which every nonzero element is invertible.
The field axioms say that a set with operations and satisfies:
- is a commutative ring.
- satisfies the unital ring axiom with identity .
- Every with is a unit.
Remarks
Equivalently, the group of units is . A structure satisfying these axioms is precisely a field.