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'Euclidean domain'
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| Title of object: |
Euclidean domain |
| Canonical Name: |
EuclideanRing |
| Type: |
Definition |
| Created on: |
2002-05-27 22:59:18 |
| Modified on: |
2006-07-31 15:45:55 |
| Classification: |
msc:13F07 |
| Synonyms: |
Euclidean domain=Euclidean ring |
Revision comment (for changes between this and next version):
Preamble:
\usepackage{amssymb}
\newcommand{\Z}{\mathbb{Z}}
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Content:
\PMlinkescapeword{even}
A \emph{Euclidean domain} is an integral domain where a Euclidean valuation has been defined.
Any Euclidean domain is also a principal ideal domain and therefore also a unique factorization domain.
But even more important, on Euclidean domains we can define gcd and use Euclid's algorithm.
Examples of Euclidean domains are the rings $\Z$ and the polynomial ring on one variable $F[x]$ where $F$ is a field. |
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