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cancellation ring

Type of Math Object: 
Definition
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Mathematics Subject Classification

13-00 no label found

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According to the entry "prime ring", cancellation rings must also be commutative. Either my entry or this entry should be edited so that the statements match.

A comparison with cancellative semigroups suggest
that commutativity is not essential for cancellation.

Then what is the difference, if any, between a prime ring and a cancellation ring?

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