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 -