ON D-ALGEBRAS BETWEEN D[X] AND Int(D)

Jean-Luc Chabert; Ali Tamoussit

doi:10.1216/jca.2024.16.173

Abstract

The aim of this paper is to study conditions on an integral domain $D$ such that any $D$ -algebra between the polynomial ring $D\lbrack X\rbrack$ and the ring of integer-valued polynomials $\mathrm{Int}(D)$ is (locally) free. These results are then extended to several indeterminates.

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Jean-Luc Chabert. Ali Tamoussit. "ON $D$ -ALGEBRAS BETWEEN $D\lbrack X\rbrack$ AND $\mathrm{Int}(D)$ ." J. Commut. Algebra 16 (2) 173 - 181, Summer 2024. https://doi.org/10.1216/jca.2024.16.173

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Received: 18 July 2023; Revised: 11 October 2023; Accepted: 30 October 2023; Published: Summer 2024

First available in Project Euclid: 16 May 2024

Digital Object Identifier: 10.1216/jca.2024.16.173

Subjects:

Primary: 13F20

Secondary: 13F05 , 16D40

Keywords: integer-valued polynomials , locally essential domains , locally free modules , regular basis

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