Precover completing domains and approximations

In this paper, we introduce an -precover completing domain , with being a class of modules and not necessarily a single module, and then investigate when every module in has an -preenvelope. Epic and monic -preenvelopes are also investigated. This study plays a key role in setting a general framewor...

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Published in:Communications in algebra 2023-03, Vol.51 (3), p.915-929
Main Authors: Amzil, Houda, Bennis, Driss, Rozas, J. R. García, Oyonarte, Luis
Format: Article
Language:English
Subjects:
Domains
Modules
precover completing domains
Precovers
preenvelopes
R-Mittag-Leffler modules
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Bennis, Driss
Rozas, J. R. García
Oyonarte, Luis
description In this paper, we introduce an -precover completing domain , with being a class of modules and not necessarily a single module, and then investigate when every module in has an -preenvelope. Epic and monic -preenvelopes are also investigated. This study plays a key role in setting a general framework for several classical results. Then, for a class of finitely generated modules , we introduce the notion of -R-Mittag-Leffler modules as a natural extension of R-Mittag-Leffler modules. This enabled us to find easier proofs of some known results and also establish new ones.
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subjects Domains
Modules
precover completing domains
Precovers
preenvelopes
R-Mittag-Leffler modules
title Precover completing domains and approximations
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