Flat envelopes in commutative rings
type: Item
instance of: scholarly article
title: Flat envelopes in commutative rings
zbMATH Open document ID: 0667.13005
DOI: 10.1007/BF02767358
author: J. Asensio Mayor
author: Juan Martínez Hernández
published in: Israel Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: The authors take up the notion of a flat preenvelope and a flat envelope of a module over an associative ring R, first introduced by \textit{E. E. Enochs} [Isr. J. Math. 39, 189-209 (1981; Zbl 0464.16019)], and persue some of his results. Particularly, the relation between R being coherent and the existence of envelopes and preenvelopes is discussed. If R is commutative and its localization for each prime ideal has a finite weak global dimension, then every R-module has a flat envelope if and only if R is coherent with a weak global dimension of \(at\quad most\quad 2\).
Mathematics Subject Classification ID: 13C11
Mathematics Subject Classification ID: 16D40
zbMATH DE Number: 4091628
zbMATH Keywords: coherent ring
zbMATH Keywords: flat preenvelope
zbMATH Keywords: flat envelope
MaRDI profile type: Publication
cites work: Rings which have flat injective modules
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cites work: Flat and FP-Injectivity
cites work: Autour de la platitude
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cites work: Q4122006
full work available at URL: https://doi.org/10.1007/bf02767358
OpenAlex ID: W2035489676
description: scientific article; zbMATH DE number 4091628