Local Rings of Cohen-Macaulay $F$-Rational Rings Are $F$-Rational

F-rational Rings Have Rational Singularities

It is proved that an excellent local ring of prime characteristic in which a single ideal generated by any system of parameters is tightly closed must be pseu-dorational. A key point in the proof is a characterization of F-rational local rings as those Cohen-Macaulay local rings (R; m) in which the local cohomology module H d m (R) (where d is the dimension of R) have no submodules stable under...

Local Rings of Finite Cohen-macaulay Type

Let (R,m) be a local Cohen-Macaulay ring whose m-adic completion R̂ has an isolated singularity. We verify the following conjecture of F.-O. Schreyer: R has finite Cohen-Macaulay type if and only if R̂ has finite Cohen-Macaulay type. We show also that the hypersurface k[[x0, . . . , xd]]/(f) has finite Cohen-Macaulay type if and only if k [[x0, . . . , xd]]/(f) has finite Cohen-Macaulay type, whe...

On Cohen-Macaulay rings

In this paper, we use a characterization of R-modules N such that fdRN = pdRN to characterize Cohen-Macaulay rings in terms of various dimensions. This is done by setting N to be the dth local cohomology functor of R with respect to the maximal ideal where d is the Krull dimension of R.

0 on Cohen - Macaulay Rings of Invariants

We investigate the transfer of the Cohen-Macaulay property from a commutative ring to a subring of invariants under the action of a finite group. Our point of view is ring theoretic and not a priori tailored to a particular type of group action. As an illustration, we briefly discuss the special case of multiplicative actions, that is, actions on group algebras k[Z n ] via an action on Z n .

Cohen-macaulay F -injective Homomorphisms