Difference between revisions of "Integral domain"
(New page: An '''integral domain''' is a commutative domain. More explicitly a ring, <math>R</math>, is an integral domain if: * it is commutative, * <math>0\neq 1<...)
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Revision as of 16:26, 5 September 2008
More explicitly a ring, , is an integral domain if:
- it is commutative,
- (where and are the additive and multiplicative identities, respectively)
- and it contains no zero divisors (i.e. there are no nonzero such that ).
Some common examples of integral domains are:
- The ring of integers.
- Any field.
- The p-adic integers, .
- For any integral domain, , the polynomial ring is also an integral domain.
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