A universal coefficient theorem for Gauss's Lemma
Commutative Algebra
2012-10-25 v2
Abstract
We prove a version of Gauss's Lemma. It recursively constructs polynomials {c_k} for k=0,1,...,m+n, in Z[a_i,A_i,b_j,B_j] for i=0,...,m, and j=0,1,...,n, having degree at most (m+n choose m) in each of the four variable sets, such that whenever {A_i},{B_j},{C_k} are the coefficients of polynomials A(X),B(X),C(X) with C(X)=A(X)B(X) and 1 = a_0 A_0 +...+ a_m A_m = b_0 B_0 +...+ b_n B_n, then one also has 1 = c_0 C_0 +...+ c_{m+n} C_{m+n}.
Cite
@article{arxiv.1209.6307,
title = {A universal coefficient theorem for Gauss's Lemma},
author = {William Messing and Victor Reiner},
journal= {arXiv preprint arXiv:1209.6307},
year = {2012}
}
Comments
Minor edits; version to appear in J. Commutative Algebra