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 non-Noetherian commutative ring where they don't, but prove that they do for any Noetherian commutative ring. For non-commutative 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.
|Number of pages||21|
|Journal||Advances in Mathematics|
|Early online date||23 Jul 2019|
|Publication status||Published - 1 Oct 2019|
- Derived categories
- Finite dimensional algebras
- Finitistic dimension conjecture
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Professor Jeremy C Rickard
- School of Mathematics - Professor of Mathematics
- Pure Mathematics
Person: Academic , Member