𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Indecomposable Gorenstein Modules of Odd Rank

✍ Scribed by Christel Rotthaus; Dana Weston; Roger Wiegand

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
60 KB
Volume
214
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

Let R, m be a local Cohen᎐Macaulay ring with m-adic completion R. A Gorenstein R-module is a non-zero finitely generated R-module whose m-adic completion is isomorphic to a direct sum of copies of the canonical module .

R

The rank of the Gorenstein module G is the positive integer r such that Λ†Ε½ . G ( r ΠΈ the direct sum of r copies of . In this note we show that for any Λ†R R given positive integer r there is a Cohen᎐Macaulay ring R with an indecomposable Gorenstein module G of rank r.

πŸ“œ SIMILAR VOLUMES

Gorenstein Flat Covers of Modules over G
Gorenstein Flat Covers of Modules over Gorenstein Rings
✍ Edgar Enochs; Jinzhong Xu πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 220 KB

A left and right Noetherian ring R is called Gorenstein if both R and R have R R finite injective dimensions. These rings were studied by Bass for the commutative case and Iwanaga for the noncommutative case. In this paper, we define Gorenstein flat modules over a Gorenstein ring. These modules are

Gorenstein modules of finite length
Gorenstein modules of finite length
✍ Michael Kunte πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 235 KB

In Commutative Algebra structure results on minimal free resolutions of Gorenstein modules are of classical interest. We define Symmetrically Gorenstein modules of finite length over the weighted polynomial ring via symmetric matrices in divided powers. We show that their graded minimal free resolu

On the Number of Injective Indecomposabl
On the Number of Injective Indecomposable Modules
✍ Hans-Heinrich Brungs; GΓΌnter TΓΆrner πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 158 KB

For every natural number m, there exists a noncommutative valuation ring R with a completely prime ideal P so that there are exactly m nonisomorphic indecomposable injective right R-modules with P as associated prime ideal.

Indecomposable Decompositions of Finitel
Indecomposable Decompositions of Finitely Presented Pure-Injective Modules
✍ JosΓ© L. GΓ³mez Pardo; Pedro A. Guil Asensio πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 171 KB

However, while a right ⌺-pure-injective ring is semiprimary with maximum condition on annihilator right ideals, a right pure-injective ring is only Von Neumann regular modulo the radical with the idempotent-lifting property 200