Construction of totally reflexive modules from an exact pair of zero divisors

Details Construction of totally reflexive modules from an exact pair of zero divisors Construction of totally reflexive modules from an exact pair of zero divisors

2010-02-02

arxiv.org/abs/1002.0419v1

Mathematics

Commutative Algebra

15 pages

Scientific paper

Let A be a local ring which admits an exact pair x,y of zero divisors as defined by Henriques and Sega. Assuming that this pair is regular and that there exists a regular element on the A-module A/(x,y), we explicitly construct an infinite family of non-isomorphic indecomposable totally reflexive A-modules. In this setting, our construction provides an answer to a question raised by Christensen, Piepmeyer, Striuli, and Takahashi. Furthermore, we compute the module of homomorphisms between any two given modules from the infinite family mentioned above.

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