Indecomposable modules of large rank over Cohen-Macaulay local rings

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.

Rank One Maximal Cohen-macaulay Modules Over

Indecomposable Cohen-macaulay Modules and Their Multiplicities

The main aim of this paper is to find a large class of rings for which there are indecomposable maximal Cohen-Macaulay modules of arbitrary high multiplicity (or rank in the case of domains).

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...

Direct-sum decompositions over one-dimensional Cohen-Macaulay local rings

1 Alberto Facchini, Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Belzoni 7, I-35131 Padova, Italy, [email protected] 2 Wolfgang Hassler, Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Heinrichstraße 36/IV, A-8010 Graz, Austria, [email protected] 3 Lee Klingler, Department of Mathematical Sciences, Florida Atlanti...