Prime links in Noetherian rings
type: Item
instance of: scholarly article
title: Prime links in Noetherian rings
zbMATH Open document ID: 0786.16010
published in: Bulletin of the Iranian Mathematical Society
publication date: 1993-08-08T00:00:00Z
review text: It is proved that for a localizable prime ideal \(P\) of a noetherian ring \(R\), either \(P_ P = 0\), or that \(P\) is linked to itself and that its clique consists of \(P\) alone. In the special case when \(R\) is a noetherian prime ring that is a maximal order in its simple artinian quotient ring, any reflexive prime ideal \(P\), being localizable, is thus linked to itself, and the link is via \(P^{(2)}\), the second symbolic power of \(P\) in the sense of \textit{A. Goldie} [J. Algebra 5, 89-105 (1967; Zbl 0154.288)].
reviewed by: Günter Krause
Mathematics Subject Classification ID: 16P40
Mathematics Subject Classification ID: 16P50
Mathematics Subject Classification ID: 16D25
Mathematics Subject Classification ID: 16U20
zbMATH DE Number: 179491
zbMATH Keywords: localizable prime ideal
zbMATH Keywords: noetherian ring
zbMATH Keywords: clique
zbMATH Keywords: noetherian prime ring
zbMATH Keywords: maximal order
zbMATH Keywords: simple artinian quotient ring
zbMATH Keywords: reflexive prime ideal
zbMATH Keywords: link
zbMATH Keywords: symbolic power
author: Ahmad Haghany
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 179491