Gauss's lemma: Difference between revisions
(New page: ==Statement== Gauss's lemma states that, in a gcd domain, we have the following: * A product of primitive polynomials is primitive. * The content of a...) |
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Revision as of 16:46, 1 February 2009
Statement
Gauss's lemma states that, in a gcd domain, we have the following:
- A product of primitive polynomials is primitive.
- The content of a product of polynomials is the product of their contents (upto associates).
Related facts
Applications
- Unique factorization is polynomial-closed: The polynomial ring over a unique factorization domain is again a unique factorization domain. The proof of this is a direct consequence of Gauss's lemma.