Plane modules and distributive rings
type: Item
instance of: scholarly article
title: Plane modules and distributive rings
zbMATH Open document ID: 0814.16008
DOI: 10.1007/BF01058215
published in: Ukrainian Mathematical Journal
publication date: 1994-11-10T00:00:00Z
review text: The aim of this paper is to prove the equivalence of the following conditions for a semiprime ring \(R\) which is entire over its center: (1) \(R\) is a right distributive ring (this means that the lattice of right ideals of \(R\) is distributive); (2) \(R\) is a left distributive ring; (3) \(\text{w.gl.dim}(R)\leq 1\) and the set \(R \setminus P\) is a right (or left) Ore set for any prime ideal \(P\) of \(R\).
Mathematics Subject Classification ID: 16E10
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16U20
Mathematics Subject Classification ID: 06D05
Mathematics Subject Classification ID: 16D25
zbMATH DE Number: 652246
zbMATH Keywords: semiprime ring
zbMATH Keywords: right distributive ring
zbMATH Keywords: lattice of right ideals
zbMATH Keywords: left distributive ring
zbMATH Keywords: Ore set
author: A. A. Tuganbaev
reviewed by: Toma Albu
MaRDI profile type: Publication
cites work: A Remark on Arithmetical Rings
cites work: Rings with flat right ideals and distributive rings
cites work: Q3754766
cites work: Q4744417
cites work: Modules Whose Lattice of Submodules is Distributive
cites work: Rings with distributive lattice of right ideals.
full work available at URL: https://doi.org/10.1007/bf01058215
OpenAlex ID: W2999844435
description: scientific article; zbMATH DE number 652246