Finite injective dimension over rings with Noetherian cohomology

Details Finite injective dimension over rings with Noetherian cohomology Finite injective dimension over rings with Noetherian cohomology

2011-09-13

arxiv.org/abs/1109.2814v1

Mathematics

Commutative Algebra

11 pages

Scientific paper

We study rings which have Noetherian cohomology under the action of a ring of cohomology operators. The main result is a criterion for a complex of modules over such a ring to have finite injective dimension. This criterion generalizes, by removing finiteness conditions, and unifies several previous results. In particular we show that for a module over a ring with Noetherian cohomology, if all higher self-extensions of the module vanish then it must have finite injective dimension. Examples of rings with Noetherian cohomology include commutative complete intersection rings and finite dimensional cocommutative Hopf algebras over a field.

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