Serial rings with right Krull dimension one
type: Item
instance of: scholarly article
title: Serial rings with right Krull dimension one
zbMATH Open document ID: 0621.16025
DOI: 10.1016/0021-8693(87)90142-6
published in: Journal of Algebra
publication date: 1987-01-01T00:00:00Z
review text: Let R be a serial ring, i.e. R is a direct sum of uniserial right ideals and R is a direct sum of uniserial left ideals. The paper starts by establishing some general properties of R and its modules. It is shown that R/Z(R) is non-singular where Z(R) is the right singular ideal of R, and every non-singular uniform R-module is uniserial. Then uniseral R- modules with Krull dimension are studied, and it is shown that R has right Krull dimension 1 if and only if R has left Krull dimension 1. These results are applied to the special case in which R is a non- singular serial ring of Krull dimension 1, and a triangular matrix representation is given for such rings.
Mathematics Subject Classification ID: 16L30
Mathematics Subject Classification ID: 16P60
Mathematics Subject Classification ID: 16Dxx
zbMATH DE Number: 4006479
zbMATH Keywords: serial ring
zbMATH Keywords: direct sum of uniserial right ideals
zbMATH Keywords: right singular ideal
zbMATH Keywords: uniseral R-modules
zbMATH Keywords: right Krull dimension
zbMATH Keywords: left Krull dimension
author: Mary H. Upham
reviewed by: A. W. Chatters
MaRDI profile type: Publication
full work available at URL: 0021-8693(87)90142-6
OpenAlex ID: W2037371989
cites work: The structure of serial rings
cites work: Q4101984
cites work: Krull dimension
cites work: Jacobson's conjecture and modules over fully bounded Noetherian rings
cites work: Serial Right Noetherian Rings
cites work: Coherent Rings and Fp -Injective Modules
cites work: Serial rings and finitely presented modules
description: scientific article; zbMATH DE number 4006479