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![[parent]](http://images.planetmath.org:8080/images/uparrow.png)
example of PID
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(Example)
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Important examples of principal ideal domains:
- The ring of the integers
 .
- The ring of polynomials in one variable over a field, i.e. a ring of the form
![$ \mathbb{F}[X]$](http://images.planetmath.org:8080/cache/objects/4175/l2h/img2.png "$ \mathbb{F}[X]$") , where
 is a field. Note that the ring of polynomials in more than one variable over a field is never a PID.
Both of these examples are actually examples of Euclidean rings, which are always PIDs. There are, however, more complicated examples of PIDs which are not Euclidean rings.
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"example of PID" is owned by sleske.
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Cross-references: Euclidean rings, field, variable, polynomials, integers, ring, principal ideal domains
There is 1 reference to this entry.
This is version 2 of example of PID, born on 2003-04-10, modified 2003-09-11.
Object id is 4175, canonical name is ExampleOfPID.
Accessed 2235 times total.
Classification:
| AMS MSC: | 13G05 (Commutative rings and algebras :: Integral domains) |
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Pending Errata and Addenda
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