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Axiom requiring multiplication in a ring to be commutative.
The commutative ring axiom asserts that multiplication satisfies
A commutative ring is a ring satisfying this axiom. Whether rings are required to have a multiplicative identity is a separate convention.
A ring is a set equipped with two binary operations and such that:
These conditions are often summarized as the ring axioms. Many texts additionally impose a multiplicative identity, leading to a unital ring; commutativity of multiplication leads to a commutative ring.