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cancellation ring (Definition)

A ring $ R$ is a cancellation ring if for all $ a,b \in R$, if $ a \cdot b = 0$ then either $ a=0$ or $ b=0$.



"cancellation ring" is owned by djao. [ full author list (2) | owner history (1) ]
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See Also: integral domain, zero divisor
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Cross-references: ring
There are 5 references to this entry.

This is version 3 of cancellation ring, born on 2001-10-20, modified 2002-07-25.
Object id is 421, canonical name is CancellationRing.
Accessed 5341 times total.

Classification:
AMS MSC: 13-00 (Commutative rings and algebras :: General reference works )
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commutativity by Wkbj79 on 2006-08-20 12:41:41
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.
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