Finite injective dimension over rings with Noetherian cohomology

Date

2012

Authors

Burke, Jesse

Journal Title

Journal ISSN

Volume Title

Publisher

International Press

Abstract

We study rings that have Noetherian cohomology over a ring of cohomology operators. Examples of such rings include commutative complete intersection rings and finite-dimensional cocommutative Hopf algebras. The main result is a criterion for a complex of modules over a ring with Noetherian cohomology to have finite injective dimension. The criterion implies in particular that for any module over such a ring, if all higher self-extensions of the module vanish, then it must have finite injective dimension. This generalizes a theorem of Avramov and Buchweitz for complete intersection rings, and a well-known theorem in the representation theory of finite groups from finitely generated to arbitrary modules.

Description

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Citation

Source

Mathematical Research Letters

Type

Journal article

Book Title

Entity type

Access Statement

Open Access

License Rights

DOI

10.4310/MRL.2012.v19.n4.a1

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