# Irreducibility of Polynomial part deux

1. Dec 10, 2012

### Square1

Ok I promise this time it is not a homework type question.

If someone could direct with a name of a theorem here, then I'll go ahead and google it, otherwise have a look. I have a chunk of notes that I'm confused about. We're not shown any proofs here or any explanations, just what is seen. It was talking about in somewhat of a "mention in passing" way so maybe I am not supposed to look too deep into it and just accept the results. Here it is...

Basically we are told that if we have a polynomial f in Z[x], if f = gh where g and h belong t Q[x], it can be shown that the coefficients can be selected to be in Z[x]. We told this is Gauss' Lemma. OK. Then it goes, we change the given polynomial into the corresponding polynomial that has the coefficients changed into elements of a prime congruence class. g and h are defined the same, then "f-bar" = "g-bar" times "h-bar". If p prime is chosen right, it shows that if "f-bar" is irreducible, then f is irreducible.

I'll start by asking does anyone know what this is describing, and if we have a name for it?

Last edited: Dec 10, 2012
2. Dec 10, 2012

### Square1

Ok just found it actually. Case closed -.-

3. Dec 12, 2012

### mathwonk

you might look at some of my free algebra notes on my website. see my public profile for my web address under contact info. or just click on my name at left and the pulldown menu gives a link to it.

4. Dec 12, 2012

### Square1

Thanks for the suggestion, roy :) . I'll keep this mind.