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Seminario Dottorato: “Covers and envelopes of modules”

Wednesday 27 March 2019, h.14:30 - Room 2BC30 - Giovanna Giulia Le Gros

ARGOMENTI: Seminars Ph.D. Program

Wednesday 27 March 2019 h.14:30, Room 2BC30
Giovanna Giulia Le Gros (Padova, Dip. Mat.)
“Covers and envelopes of modules”

Abstract
Approximation theory of modules is the study of left or right approximations of modules, also known as covers or envelopes, with respect to certain classes of modules. For a class C of R-modules, the aim is to characterise the rings over which every module has a C-cover or a C-envelope and furthermore to characterise the class C itself. For example, if one considers the class of injective modules, then it is well-known that every module has an injective envelope (or injective hull). Instead, Bass proved that projective covers rarely exist and characterised the rings over which every module admits a projective cover, which are known as perfect rings. Moreover, precovers and preenvelopes are strongly related to the notion of a cotorsion pair, which is a pair of Ext-orthogonal classes in the category of R-modules.
The aim of this talk is to give a basic introduction to the theory of covers and envelopes, and to describe them with respect to some well-known classes of R-modules, along with a review of concepts in homological algebra that will be useful in this exposition.

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