Ring Constructions and Generation of the Unbounded Derived Module Category

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Abstract

We consider the smallest triangulated subcategory of the unbounded derived module category of a ring that contains the injective modules and is closed under set indexed coproducts. If this subcategory is the entire derived category, then we say that injectives generate for the ring. In particular, we ask whether, if injectives generate for a collection of rings, do injectives generate for related ring constructions, and vice versa. We provide sufficient conditions for this statement to hold for various constructions including recollements, ring extensions and module category equivalences.

OriginalsprogEngelsk
TidsskriftAlgebras and Representation Theory
Vol/bind26
Nummer1
Sider (fra-til)281-315
Antal sider35
ISSN1386-923X
DOI
StatusUdgivet - feb. 2023
Udgivet eksterntJa

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