A universal coefficient theorem for gauss's lemma

摘要

We shall prove a version of Gau?'s lemma. It works in Z[a,A, b,B] where a = {a_i}~m _(i=0), A = {A_i}~m _(i=0), b = {b_i}~n _(j=0), B = {B_j}~n _(j=0), and constructs polynomials {c_k}k=0,..., m+n of degree at most in each variable set a,A, b,B, with this property: setting for elements a_i,A_j, b_j, B_j in any commutative ring R satisfying, the elements c_k = ck(a_i,A_i, b_j,B_j) satisfy.