Formally we say that a ring is a Euclidean domain if:
- It is an integral domain.
- There a function called a Norm such that for all nonzero there are such that and either or .
Some common examples of Euclidean domains are:
- The ring of integers with norm given by .
- The ring of Gaussian integers with norm given by .
- The ring of polynomials over any field with norm given by .
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