Ring Constructions and Generation of the Unbounded Derived Module Category

TY - JOUR

T1 - Ring Constructions and Generation of the Unbounded Derived Module Category

AU - Cummings, Charley

PY - 2023/2

Y1 - 2023/2

N2 - 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.

AB - 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.

KW - Derived categories

KW - Homological conjectures

KW - Recollements

UR - http://www.scopus.com/inward/record.url?scp=85118674339&partnerID=8YFLogxK

U2 - 10.1007/s10468-021-10094-2

DO - 10.1007/s10468-021-10094-2

M3 - Journal article

SN - 1386-923X

VL - 26

SP - 281

EP - 315

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

IS - 1

ER -