Integral domain
From AoPSWiki
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
![R[x]](http://alt2.artofproblemsolving.com/Forum/latexrender/pictures/a/e/d/aed27a7f5a83471065d6c6e564b9cc83834e7964.gif)
is also an integral domain.
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