کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8896216 | 1630412 | 2018 | 32 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Test sets for polynomials: n-universal subsets and Newton sequences
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let E be a subset of an integral domain D with quotient field K. A subset S of E is said to be an n-universal subset of E if every integer-valued polynomial f(X)âK[X] on S (that is, such that f(S)âD), with degree at most n, is integer-valued on E (that is, f(E)âD). A sequence a0,â¦,an of elements of E is said to be a Newton sequence of E of length n if, for each kâ¤n, the subset {a0,â¦,ak} is a k-universal subset of E. Our main results concern the case where D is a Dedekind domain, where both notions are strongly linked to p-orderings, as introduced by Bhargava. We extend and strengthen previous studies by Volkov, Petrov, Byszewski, Fra̧czyk, and Szumowicz that concerned only the case where E=D. In this case, but also if E is an ideal of D, or if E is the set of prime numbers >n+1 (in D=Z), we prove the existence of sequences in E of which n+2 consecutive terms always form an n-universal subset of E.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 502, 15 May 2018, Pages 277-314
Journal: Journal of Algebra - Volume 502, 15 May 2018, Pages 277-314
نویسندگان
Paul-Jean Cahen, Jean-Luc Chabert,