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A commutative discrete cancellation ring is a discrete cancellation ring that is also a commutative ring
The integers are a commutative discrete cancellation ring.
The rational numbers are a commutative discrete cancellation ring.
Every discrete integral domain is a commutative discrete cancellation ring.
Every commutative discrete division ring is a commutative discrete cancellation ring.
Every commutative discrete reciprocal ring is a commutative discrete cancellation ring.