Difference between revisions of "Integral domain"
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Revision as of 17:26, 5 September 2008
An integral domain is a commutative domain.
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
).
Examples
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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