ABSTRACT
Now that we have Gauss’ lemma in hand we can look at cyclotomic polynomials again, not as polynomials with coefficients in various fields, but as universal things, having coefficients in Z. [1] Most of this discussion is simply a rewrite of the earlier discussion with coefficients in fields, especially the case of characteristic 0, paying attention to the invocation of Gauss’ lemma. A new point is the fact that the coefficients lie in Z. Also, we note the irreducibility of Φp(x) for prime p in both Z[x] and Q[x], via Eisenstein’s criterion (and Gauss’ lemma, again).
