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

Henrik Granau Holm

doi:10.1112/blms/bdq104

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

9 Citations (Scopus)

Abstract

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.

Original language	English
Journal	Bulletin of the London Mathematical Society
Volume	43
Issue number	2
Pages (from-to)	278-288
Number of pages	11
ISSN	0024-6093
DOIs	https://doi.org/10.1112/blms/bdq104
Publication status	Published - Apr 2011

Access to Document

10.1112/blms/bdq104

Cite this

@article{df23595c7a58430aa5c9267d3d47e8ec,

title = "Construction of totally reflexive modules from an exact pair of zero divisors",

abstract = "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.",

author = "Holm, {Henrik Granau}",

year = "2011",

month = apr,

doi = "10.1112/blms/bdq104",

language = "English",

volume = "43",

pages = "278--288",

journal = "Bulletin of the London Mathematical Society",

issn = "0024-6093",

publisher = "Oxford University Press",

number = "2",

}

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 -

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

Abstract

Access to Document

Fingerprint

Cite this