Difference between revisions of "Unique factorization domain"
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Revision as of 21:24, 23 August 2009
A unique factorization domain is an integral domain in which an analog of the fundamental theorem of arithmetic holds. More precisely an integral domain is a unique factorization domain if for any element
which is not a unit:
can be written in the form
where
are (not necessarily distinct) irreducible elements in
.
- This representation is unique up to units and reordering, that is if
where
and
are all irreducibles then
and there is some permutation
of
such that for each
there is a unit
such that
.
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