Monoids of modules over rings of infinite Cohen-Macaulay type

Maximal Cohen-macaulay Modules over Hypersurface Rings

This paper is a brief survey on various methods to classify maximal Cohen-Macaulay modules over hypersurface rings. The survey focuses on the contributions in this topic of Dorin Popescu together with his collaborators.

Cohen-macaulay Modules and Holonomic Modules over Filtered Rings

We study Gorenstein dimension and grade of a module M over a filtered ring whose assosiated graded ring is a commutative Noetherian ring. An equality or an inequality between these invariants of a filtered module and its associated graded module is the most valuable property for an investigation of filtered rings. We prove an inequality G-dimM ≤ G-dimgrM and an equality gradeM = grade grM , whe...

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...

Rank One Maximal Cohen-macaulay Modules Over

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.