Various properties of a general class of integer-valued polynomials. (English) Zbl 1508.13018
Authors’ abstract: In this paper, we study various properties for some classes of domains that are generalizations of integer-valued polynomial rings. For \(D\) an integral domain with quotient field \(K\) and \(E\) a subset of \(K\), one defines as usual Int(\(E, D\))\( := \{ f\in K[X] : f (E)\subseteq D \}\). If \(R\) is an integral domain containing \(D\), then we define Int\(_R\)(\(E, D\)) \(:= \{ f\in R[X] : f (E)\subseteq D \}\), which is called the ring of \(D\)-valued \(R\)-polynomials over \(E\). Among other things, we investigate various properties and facts around the rings Int\(_R\)(\(E, D\)), such as localization, (faithful) flatness, Krull dimension and some other transfer properties.
Reviewer: François Couchot (Caen)
MSC:
| 13F05 | Dedekind, Prüfer, Krull and Mori rings and their generalizations |
| 13F20 | Polynomial rings and ideals; rings of integer-valued polynomials |
| 13B30 | Rings of fractions and localization for commutative rings |
| 16D40 | Free, projective, and flat modules and ideals in associative algebras |
Keywords:
integer-valued polynomials; localization; prime ideals; (faithfully) flat modules; Krull dimensionReferences:
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