Beyond totally reflexive modules and back A survey on gorenstein dimensions

Lars Winther Christensen; Hans Bjorn Foxby; Henrik Holm

doi:10.1007/978-1-4419-6990-3_5

Beyond totally reflexive modules and back A survey on gorenstein dimensions

Lars Winther Christensen, Hans Bjorn Foxby, Henrik Holm

Mathematics and Statistics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

48 Scopus citations

Abstract

Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein homological dimensions for modules over commutative rings. The account includes the theory's connections with relative homological algebra and with studies of local ring homomorphisms. It ends close to the starting point: with a characterization of Gorenstein rings in terms of total acyclicity of complexes.

Original language	English
Title of host publication	Commutative Algebra
Subtitle of host publication	Noetherian and Non-Noetherian Perspectives
Publisher	Springer New York
Pages	101-143
Number of pages	43
ISBN (Print)	9781441969897
DOIs	https://doi.org/10.1007/978-1-4419-6990-3_5
State	Published - 2011

Access to Document

10.1007/978-1-4419-6990-3_5

Cite this

@inbook{5f75ec2774dc42889be1295da0d92c77,

title = "Beyond totally reflexive modules and back A survey on gorenstein dimensions",

abstract = "Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein homological dimensions for modules over commutative rings. The account includes the theory's connections with relative homological algebra and with studies of local ring homomorphisms. It ends close to the starting point: with a characterization of Gorenstein rings in terms of total acyclicity of complexes.",

author = "Christensen, {Lars Winther} and Foxby, {Hans Bjorn} and Henrik Holm",

year = "2011",

doi = "10.1007/978-1-4419-6990-3_5",

language = "English",

isbn = "9781441969897",

pages = "101--143",

booktitle = "Commutative Algebra",

publisher = "Springer New York",

}

TY - CHAP

T1 - Beyond totally reflexive modules and back A survey on gorenstein dimensions

AU - Christensen, Lars Winther

AU - Foxby, Hans Bjorn

AU - Holm, Henrik

PY - 2011

Y1 - 2011

N2 - Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein homological dimensions for modules over commutative rings. The account includes the theory's connections with relative homological algebra and with studies of local ring homomorphisms. It ends close to the starting point: with a characterization of Gorenstein rings in terms of total acyclicity of complexes.

AB - Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein homological dimensions for modules over commutative rings. The account includes the theory's connections with relative homological algebra and with studies of local ring homomorphisms. It ends close to the starting point: with a characterization of Gorenstein rings in terms of total acyclicity of complexes.

UR - http://www.scopus.com/inward/record.url?scp=84867681490&partnerID=8YFLogxK

U2 - 10.1007/978-1-4419-6990-3_5

DO - 10.1007/978-1-4419-6990-3_5

M3 - Chapter

AN - SCOPUS:84867681490

SN - 9781441969897

SP - 101

EP - 143

BT - Commutative Algebra

PB - Springer New York

ER -

Beyond totally reflexive modules and back A survey on gorenstein dimensions

Abstract

Access to Document

Other files and links

Fingerprint

Cite this