C2-rings and the FGF-conjecture
type: Item
instance of: scholarly article
zbMATH Open document ID: 1014.16004
publication date: 2003-04-14T00:00:00Z
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16L60
Mathematics Subject Classification ID: 16D40
Mathematics Subject Classification ID: 16E50
zbMATH DE Number: 1639885
zbMATH Keywords: C2-rings
zbMATH Keywords: FGF-rings
zbMATH Keywords: FGF-conjecture
zbMATH Keywords: quasi-Frobenius rings
zbMATH Keywords: continuous rings
zbMATH Keywords: direct summands
zbMATH Keywords: free modules
author: W. Keith Nicholson
author: Mohamed F. Yousif
MaRDI profile type: Publication
title: C2-rings and the FGF-conjecture
review text: The C2-property was introduced by Utumi in his study of continuous rings, and a ring \(R\) is called a right C2-ring when every right ideal of \(R\) which is isomorphic to a direct summand of \(R_R\) is itself a direct summand. The authors make a survey of recent results on C2-rings, with special attention devoted to the impact of this condition on the FGF problem, which asks whether a ring for which every finitely generated right module embeds in a free module (called a right FGF-ring) is necessarily quasi-Frobenius. Among other results, they show that in order to give an affirmative answer to the FGF problem it is enough to prove that every right FGF-ring is a right C2-ring.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00043].
reviewed by: José L. Gómez-Pardo
description: scientific article; zbMATH DE number 1639885