Topic
Integer-valued polynomial
About: Integer-valued polynomial is a research topic. Over the lifetime, 41 publications have been published within this topic receiving 300 citations.
Papers
TL;DR: In this paper, the authors generalize some known results on integer-valued polynomial rings over Krull domains, Prufer v-multiplication domains, and Mori domains, using the tools of t-closure and associated primes.
Abstract: Given an integral domain D with quotient field K, the ring of integer-valued polynomials on D is the subring {f(X) ∈ K[X]: f(D) ⊂ D} of the polynomial ring K[X] Using the tools of t-closure and associated primes, we generalize some known results on integer-valued polynomial rings over Krull domains, Prufer v-multiplication domains, and Mori domains
21 citations
TL;DR: In this paper, it was shown that the ring Int (D X ) of integer-valued polynomials on D X is the free polynomial complete extension of D generated by X, provided only that D is not a finite field.
17 citations
Journal Article•
TL;DR: In this article, the authors studied the ring of integer-valued polynomials on the quotient field K of any valuation domain and showed that if E is precompact, then Int(E, V) has properties similar to those of the classical ring Int(Z).
Abstract: Let V be any valuation domain and let E be a subset of the quotient field K of V. We study the ring of integer-valued polynomials on E, that is, Int(E, V)={fK[X]｜f(E)⊆V}. We show that, if E is precompact, then Int(E, V) has many properties similar to those of the classical ring Int(Z).In particular, Int(E, V) is dense in the ring of continuous functions C(E, V); each finitely generated ideal of Int(E, V) may be generated by two elements; and finally, Int(E, V) is a Prufer domain.
17 citations
15 Jan 2009
16 citations
TL;DR: In this paper, the authors extend the definition of Int K -decomposability to D-algebras and show that a D-module basis for A is also an Int K-decompositional basis for Int K (A ) if A is isomorphic to Int K(A ) ⊗ D A.
13 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2020 | 3 |
| 2018 | 4 |
| 2017 | 1 |
| 2016 | 3 |
| 2015 | 2 |