A characterization of rings with Krull dimension
type: Item
instance of: scholarly article
title: A characterization of rings with Krull dimension
zbMATH Open document ID: 0706.16013
DOI: 10.1016/0021-8693(90)90254-L
author: Dinh Van Huynh
author: Nguyen Viet Dung
author: Patrick F. Smith
published in: Journal of Algebra
publication date: 1990-01-01T00:00:00Z
review text: Many classes of rings can be, and have been, characterized by their cyclic modules. The present authors continue this line of investigation by considering rings with Krull dimension. They consider the following property: (P). Every cyclic right R-module is a direct sum of an injective module and a module containing an essential submodule with Krull dimension at most \(\alpha\). The main result is that a ring with property (P) has right Krull dimension at most \(\alpha\).
Mathematics Subject Classification ID: 16P60
Mathematics Subject Classification ID: 16D50
zbMATH DE Number: 4158878
zbMATH Keywords: cyclic modules
zbMATH Keywords: Krull dimension
zbMATH Keywords: direct sum
zbMATH Keywords: injective module
zbMATH Keywords: essential submodule
reviewed by: T. H. Lenagan
MaRDI profile type: Publication
cites work: A CHARACTERISATION OF RIGHT NOETHERIAN RINGS
cites work: A characterization of artinian rings
cites work: Q4101984
cites work: Torsion-free modules and rings
cites work: Q4104083
cites work: Krull dimension
cites work: Modules with Krull Dimension
cites work: Rings all of whose finitely generated modules are injective
cites work: SOME RINGS WHICH ARE CHARACTERISED BY THEIR FINITELY GENERATED MODULES
cites work: Rings Characterized by their Cyclic Modules
cites work: The Dual of the Notion of “Finitely Generated”
description: scientific article; zbMATH DE number 4158878