Abstract
We consider the question of whether the injective modules generate the unbounded derived category of a ring as a triangulated category with arbitrary coproducts. We give an example of a nonNoetherian commutative ring where they don't, but prove that they do for any Noetherian commutative ring. For noncommutative finite dimensional algebras the question is open, and we prove that if injectives generate for such an algebra, then the finitistic dimension conjecture holds for that algebra.
Original language  English 

Article number  106735 
Number of pages  21 
Journal  Advances in Mathematics 
Volume  354 
Early online date  23 Jul 2019 
DOIs  
Publication status  Published  1 Oct 2019 
Keywords
 Derived categories
 Finite dimensional algebras
 Finitistic dimension conjecture
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Professor Jeremy C Rickard
 School of Mathematics  Professor of Mathematics
 Pure Mathematics
 Algebra
Person: Academic , Member