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Euclidean Domains

Definition 1   An integral domain R endowed with a function d : R $ \longmapsto$ $ \mbox{${\mathbb N}$}$  $ \cup$  { - $ \infty$} is an Euclidean domain if the following two conditions hold The elements q and r are called the quotient and the remainder of a w.r.t. b (although q and r may not be unique). The function d is called the Euclidean size.

Example 1   Here are some classical examples.


next up previous
Next: The Euclidean Algorithm Up: The Euclidean Algorithm Previous: The Euclidean Algorithm
Marc Moreno Maza
2004-04-27