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

TY - JOUR

T1 - Construction of totally reflexive modules from an exact pair of zero divisors

AU - Holm, Henrik Granau

PY - 2011/4

Y1 - 2011/4

N2 - Let A be a local ring that admits an exact pair x, y of zero divisors as defined by Henriques and ega. Assuming that this pair is orthogonal and that there exists a regular element on the A-module A/(x, y), we explicitly construct an infinite family of non-isomorphic indecomposable A-modules whose minimal free resolutions are periodic of period 2, and which are totally reflexive. In this setting, our construction provides an answer to a question by Christensen, Piepmeyer, Striuli, and Takahashi. Furthermore, we compute the module of homomorphisms between any two given modules from the infinite family mentioned above.

AB - Let A be a local ring that admits an exact pair x, y of zero divisors as defined by Henriques and ega. Assuming that this pair is orthogonal and that there exists a regular element on the A-module A/(x, y), we explicitly construct an infinite family of non-isomorphic indecomposable A-modules whose minimal free resolutions are periodic of period 2, and which are totally reflexive. In this setting, our construction provides an answer to a question by Christensen, Piepmeyer, Striuli, and Takahashi. Furthermore, we compute the module of homomorphisms between any two given modules from the infinite family mentioned above.

U2 - 10.1112/blms/bdq104

DO - 10.1112/blms/bdq104

M3 - Journal article

SN - 0024-6093

VL - 43

SP - 278

EP - 288

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 2

ER -