Euclidean domain
A Euclidean domain (or Euclidean ring) is a type of ring in which the Euclidean algorithm can be used.
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
.
See also
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