Commutative rings having only a finite number of ideals
type: Item
instance of: scholarly article
title: Commutative rings having only a finite number of ideals
zbMATH Open document ID: 0564.13007
DOI: 10.1007/BF03322492
published in: Results in Mathematics
publication date: 1984-01-01T00:00:00Z
review text: The paper tries to describe all commutative rings with identity having only finitely many ideals. Obviously those rings are artinian, commutative artinian rings decompose into a direct sum of local rings. So the problem reduces to artinian rings. Their structure is well known. Proofs are provided for I. S. Cohen's structure theorems for local artinian rings (theorems 1 and 2). The proof of theorem 1 uses a ``polynomial'' version of Hensel's lemma (L 1).
Mathematics Subject Classification ID: 13C05
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13E10
Mathematics Subject Classification ID: 13H99
zbMATH DE Number: 3899039
zbMATH Keywords: local artinian rings
zbMATH Keywords: finitely many ideals
author: Horia C. Pop
reviewed by: Frank Eckstein
MaRDI profile type: Publication
cites work: Q5590141
cites work: Q5563439
cites work: On the Structure and Ideal Theory of Complete Local Rings
cites work: Q5577214
cites work: Q5509717
description: scientific article; zbMATH DE number 3899039