Ring Constructions and Generation of the Unbounded Derived Module Category
Keyword(s):
AbstractWe 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.
2015 ◽
Vol 144
(3)
◽
pp. 1015-1020
◽
2019 ◽
Vol 18
(06)
◽
pp. 1950104
◽
2014 ◽
Vol 6
(2)
◽
pp. 360-366
◽
2018 ◽
Vol 17
(11)
◽
pp. 1850218
Keyword(s):
2012 ◽
Vol 19
(spec01)
◽
pp. 821-840
◽
2016 ◽
Vol 15
(08)
◽
pp. 1650145
◽
2017 ◽
Vol 60
(4)
◽
pp. 879-890
◽
2013 ◽
Vol 11
(2)
◽
pp. 297-329
◽