On noncommutative Prüfer rings
type: Item
instance of: scholarly article
title: On noncommutative Prüfer rings
zbMATH Open document ID: 0578.16001
DOI: 10.1007/BF01210779
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: A noncommutative ring without zero divisors is called a Prüfer ring if its lattice of right ideals and its lattice of left ideals is distributive. A method is given to construct Prüfer rings, which are subrings of k(x,\(\sigma)\), the field of fractions of the skew polynomial ring k[x,\(\sigma\) ]. With this theorem, an example of an invariant Prüfer ring is given, which is the intersection of non-invariant, maximal valuation rings.
Mathematics Subject Classification ID: 16U30
Mathematics Subject Classification ID: 16W60
Mathematics Subject Classification ID: 16Dxx
Mathematics Subject Classification ID: 16U10
zbMATH DE Number: 3925019
zbMATH Keywords: lattice of right ideals
zbMATH Keywords: Prüfer rings
zbMATH Keywords: skew polynomial ring
zbMATH Keywords: maximal valuation rings
author: Joachim Graeter
MaRDI profile type: Publication
cites work: Rings with a distributive lattice of right ideals
cites work: Q4126487
cites work: Über die Bewertungen endlich dimensionaler Divisionsalgebren
cites work: Zur Theorie nicht kommutativer Prüferringe
cites work: Bewertungen nicht kommutativer Körper
cites work: Zur Bewertungstheorie nicht kommutativer Körper
cites work: Noncommutative valuations
cites work: Modules Whose Lattice of Submodules is Distributive
description: scientific article; zbMATH DE number 3925019