Integer-Valued Polynomials and Prüfer v-Multiplication Domains
✍ Scribed by Paul-Jean Cahen; Alan Loper; Francesca Tartarone
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 188 KB
- Volume
- 226
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
Let D be a domain with quotient field K. We consider the ring Int D [ f g w x Ž .
x K X ; f D : D of integer-valued polynomial rings over D. We completely Ž . characterize the domains D for which Int D is a Prufer ¨-multiplication domain.
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📜 SIMILAR VOLUMES
Let A be a Dedekind domain with finite residue fields, K it's quotient field, L a finite separable extension of K, and B the integral closure of A in L. The rings of integer-valued polynomials on A and B are known to be Pru fer domains and will be denoted by Int(A) and Int(B), respectively. We will
Let \(R\) be a Dedekind domain with field of fractions \(K, L=K(x)\) a finite separable extension of \(K\), and \(S\) the integral closure of \(R\) in \(L\). Let \(I\) be the subring of \(K[X]\) consisting of all polynomials \(g(x)\) in \(K[X]\) such that \(g(R) \subset R\), and let \(E_{x}: I \righ
Let R be a domain and K its quotient-field. For a subset S of K, let F R (S) be the set of polynomials f # K[x] with f (S ) R and define the R-closure of S as the set of those t # K for which f (t) # R for all f # F R (S ). The concept of R-closure was introduced by McQuillan (J. Number Theory 39 (1