A UNIVERSAL COEFFICIENT THEOREM FOR GAUSS'S LEMMA

作者：Messing William^*; Reiner Victor

来源：Journal of Commutative Algebra, 2013, 5(2): 299-307.

DOI：10.1216/JCA-2013-5-2-299

• Gauss lemma
• constructive

We shall prove a version of Gauss's lemma. It works in Z[a, A, b, B] where a = {a(i)}(i=0)(m), A = {A(i)}(i=0)(m), b = {b(i)}(j=0)(n), B = {B-j}(j=0)(n), and constructs polynomials {c(k)}(k=0,... ,m+n) of degree at most
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in each variable set a, A, b, B, with this property: setting
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for elements a(i), A(i), b(j), B-j in any commutative ring R satisfying
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the elements c(k) = c(k)(a(i), A(i), b(j), B-j) satisfy 1 = Sigma(k) c(k)C(k).

• 出版日期2013