Difference between revisions of "Schonemann's criterion"
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Revision as of 11:41, 18 December 2009
For a polynomial q denote by 
the residue of 
modulo 
.
Suppose the following conditions hold:
<list>
<it> 
with 
, prime, and ![$f,g\in \mathbb{Z}[X]$](http://latex.artofproblemsolving.com/7/b/8/7b8b5aecb8346c6528ad1b520a84656bb2e49a05.png)
.
<it> 
<it> 
is primitive
<it> 
is irreducible in ![$\mathbb{F}_p[X]$](http://latex.artofproblemsolving.com/1/b/6/1b69862785353c9500fcec83ebfbe95348950d6c.png)
.
<it> does not divide 
.
<\list>
Then is irreducible in ![$\mathbb{Q}[X]$](http://latex.artofproblemsolving.com/f/3/d/f3dc4b61f66a97c235268da5643f5bebbc69c9bd.png)
.
See also Eisenstein's criterion.
