Prime and principal closed ideals in polynomial rings
type: Item
instance of: scholarly article
title: Prime and principal closed ideals in polynomial rings
zbMATH Open document ID: 0702.16002
DOI: 10.1016/0021-8693(90)90210-F
author: Miguel Ferrero
published in: Journal of Algebra
publication date: 1990-01-01T00:00:00Z
review text: Let R be a prime ring with maximal right quotient ring Q and extended centroid C. The main purpose of the paper under review is to characterise those prime ideals P of the polynomial ring R[x] which satisfy \(P\cap R=0\) as the ideals of the form Q[x]f\(\cap R[x]\), where f is an irreducible element of C[x]. Ideals of the latter form but with f not necessarily irreducible are termed principal closed ideals. The paper also includes results on rings intermediate between R and Q, a decomposition theorem for principal closed ideals and applications to results transferring certain properties from R to R[x].
Mathematics Subject Classification ID: 16D25
Mathematics Subject Classification ID: 16S36
zbMATH DE Number: 4150422
zbMATH Keywords: prime ring
zbMATH Keywords: maximal right quotient ring
zbMATH Keywords: extended centroid
zbMATH Keywords: prime ideals
zbMATH Keywords: polynomial ring
zbMATH Keywords: irreducible element
zbMATH Keywords: principal closed ideals
reviewed by: David A. Jordan
MaRDI profile type: Publication
cites work: The strongly prime radical of an ore extension
cites work: Q4104083
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description: scientific article; zbMATH DE number 4150422