Existence of Totally Reflexive Modules via Gorenstein Homomorphisms

2011/01/13 by Kristen A. Beck, Beck, Kristen A.
Mathematics · #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC

paper · pdf · doi:10.48550/arxiv.1101.2658

Redundancy problem fixed. Most recent version to appear in the Journal of Commutative Algebra

arxiv created 2011/05/24 · arxiv updated 2011/05/25

Abstract

We define, via Gorenstein homomorphisms, a class of local rings over which there exist non-trivial totally reflexive modules. We also provide a general construction of such rings, which indicates their abundance.

Related

• Beyond Totally Reflexive Modules and Back
• On the number of indecomposable totally reflexive modules
• Totally reflexive modules over rings that are close to Gorenstein
• A Description of Totally Reflexive Modules for a Class of non-Gorenstein Rings
• Totally Reflexive Modules and Poincaré Series