On DICC rings
type: Item
instance of: scholarly article
title: On DICC rings
zbMATH Open document ID: 0606.13013
DOI: 10.1016/0021-8693(87)90206-7
author: Maria Contessa
published in: Journal of Algebra
publication date: 1987-01-01T00:00:00Z
review text: An R-module M, over a commutative ring R, is said to satisfy the doubly infinite chain condition (DICC) if any infinite chain of submodules of M stabilizes either to the right or to the left (or to both sides). A ring which satisfies the DICC condition as a module is called a DICC ring. The main result of this paper is that a DICC ring is either Noetherian or a direct product of an Artinian ring, and a non-Noetherian ring S with no prime ideal both minimal and maximal, and with the following four properties: (1) \(S_{red}\) is Noetherian; (2) N (the nilradical of S) is nilpotent; (3) N has DCC; (4) for each \(x\in S-N\), \(N/Sx\cap N\) has finite length.
reviewed by: Ira Papick
Mathematics Subject Classification ID: 13E99
Mathematics Subject Classification ID: 13E05
Mathematics Subject Classification ID: 13E10
zbMATH DE Number: 3979212
zbMATH Keywords: doubly infinite chain condition
zbMATH Keywords: DICC ring
MaRDI profile type: Publication
full work available at URL: 0021-8693(87)90206-7
OpenAlex ID: W1982775005
cites work: Q5603302
cites work: Injective modules over Noetherian rings
cites work: Q5735274
cites work: The Dual of the Notion of “Finitely Generated”
description: scientific article; zbMATH DE number 3979212