On weakly-Krull domains of integer-valued polynomials
type: Item
instance of: scholarly article
title: On weakly-Krull domains of integer-valued polynomials
zbMATH Open document ID: 1548.13007
author: Ali Tamoussit
author: Francesca Tartarone
published in: Ricerche di Matematica
publication date: 2024-09-10T00:00:00Z
review text: Let \(D\) be an integral domain with quotient field \(K\) and let \(\mathrm{Int}(D) := \{ f\in K [X]; f (D)\subseteq D\}\) be the ring of integer-valued polynomials over D. The paper under review deals with the question of when \(\mathrm{Int}(D)\) is a weakly-Krull domain. The main result asserts that \(\mathrm{Int}(D)\) may be weakly-Krull only in the trivial case, that is, \(\mathrm{Int}(D)\) is weakly-Krull if and only if \(\mathrm{Int}(D) = D[X]\) and \(D\) is a weakly-Krull \(UMT\)-domain. As an immediate consequences, for a Noetherian domain \(D\), \(\mathrm{Int}(D)\) is weakly-Krull if and only if \(D\) is weakly-Krull and \(\mathrm{Int}(D) = D[X]\). Also, for a domain \(D\), \(\mathrm{Int}(D)\) is an infra-Krull (resp. a generalized Krull) domain if and only if \(D\) is an infra-Krull (resp. a generalized Krull) domain and \(\mathrm{Int}(D)=D[X]\).
reviewed by: A. Mimouni
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13F05
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 7909914
zbMATH Keywords: integer-valued polynomials
zbMATH Keywords: weakly-Krull domain
MaRDI profile type: Publication
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DOI: 10.1007/S11587-022-00710-8
description: scientific article; zbMATH DE number 7909914