On flat and projective envelopes
type: Item
instance of: scholarly article
title: On flat and projective envelopes
zbMATH Open document ID: 0802.16003
author: J. Asensio Mayor
author: Juan Martínez Hernández
published in: Journal of Algebra
publication date: 1994-07-05T00:00:00Z
review text: The answer to the question as to over which rings each module has a flat envelope, is not known, but some results on this question have been obtained since 1981. This paper studies this question as well, and though a full answer is not found, the authors prove a characterization of rings over which every right module has a flat envelope which is a monomorphism. They also show that if \(R\) is a right perfect and left coherent ring, then every right \(R\)-module has a flat envelope. As corollary to this result it is found that if \(R\) is a left artinian ring, then every right \(R\)-module has a flat envelope. A final proposition proves that every right \(R\)-module has a projective (pre)envelope if and only if \(R\) is a right perfect and left coherent ring. The paper is concluded by a method to find the projective (pre)envelope of a finitely generated right module over an arbitrary left artinian ring, and an example.
Mathematics Subject Classification ID: 16D40
Mathematics Subject Classification ID: 16L30
Mathematics Subject Classification ID: 16P20
Mathematics Subject Classification ID: 16P70
zbMATH DE Number: 554132
zbMATH Keywords: preenvelope
zbMATH Keywords: flat envelope
zbMATH Keywords: right perfect rings
zbMATH Keywords: left coherent rings
zbMATH Keywords: left artinian rings
zbMATH Keywords: finitely generated right modules
reviewed by: Frieda Theron
MaRDI profile type: Publication
full work available at URL: jabr.1993.1195
OpenAlex ID: W2156412243
DOI: 10.1006/JABR.1993.1195
description: scientific article; zbMATH DE number 554132