Commutative ring axiom

Axiom requiring multiplication in a ring to be commutative.

Commutative ring axiom

The commutative ring axiom asserts that multiplication satisfies

ab=ba\qquad\text{for all }a,b\in R.

A commutative ring is a ring satisfying this axiom (and usually also the unital axiom). Commutativity is essential for the theory of prime ideals and for geometric results such as the Nullstellensatz.