Failure of splitting from module-finite extension rings.
Finitely generated Ext algebras.
Finiteness aspects of Gorenstein homological dimensions
We present an alternative way of measuring the Gorenstein projective (resp., injective) dimension of modules via a new type of complete projective (resp., injective) resolutions. As an application, we easily recover well known theorems such as the Auslander-Bridger formula. Our approach allows us to relate the Gorenstein global dimension of a ring R to the cohomological invariants silp(R) and spli(R) introduced by Gedrich and Gruenberg by proving that leftG-gldim(R) = maxleftsilp(R), leftspli(R),...
Finiteness properties of local cohomology modules (an application of D-modules to Commutative Algebra).
Fragments of almost ring theory
Frobenius et cohomologie locale