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?