The Missing Spectral Basis in Algebra and Number Theory
نویسنده
چکیده
The justified fame of the Euclidean algorithm derives from the fact that it has a much larger realm of applicability than just the integers. In particular, let K be any field and let K[x] be the corresponding integral domain of polynomials over K. Given r polynomials h1(x), h2(x), . . . , hr (x) ∈ K[x] whose greatest common divisor is 1 ∈ K (no common zeros in K), there exist polynomials b1(x), b2(x), . . . , br(x) ∈ K[x] with the property that
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عنوان ژورنال:
- The American Mathematical Monthly
دوره 108 شماره
صفحات -
تاریخ انتشار 2001