Commutative rings

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Commutative rings are rings in which multiplication is a commutative operation. Given any two elements $a$ and $b$ of a ring $R$, if $ab=ba$, then $R$ is a commutative ring. For example, $\mathbb {Z}$ is a commutative ring, as we can verify with two randomly chosen integers that their product is the same regardless of order.

Note that a ring can have commutative addition but not commutative multiplication; for that reason the definition does not reference addition. EXAMPLE OF SUCH A RING GOES HERE.