Gorenstein Projective Resolvents

Edgar Enochs; Sergio Estrada; Alina Iacob; Sinem Odabaşı

doi:10.1080/00927872.2015.1065847

Gorenstein Projective Resolvents

Edgar Enochs, Sergio Estrada, Alina Iacob, Sinem Odabaşı

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Let R be a local commutative n-Gorenstein ring. The existence of the Gorenstein projective preenvelopes for finite R-modules is known (it was proved using duality arguments). In the present article, we compute an explicit Gorenstein projective preenvelope and a right Gorenstein projective resolution of a finite R-module. In light of this knowledge, we consider left derived functors Ext_i(−, −), (Formula presented.) , and Gext_i(−, −). We prove a balance result for the Tate derived functor (Formula presented.). Finally, we get an exact sequence connecting these derived functors.

Original language	American English
Journal	Communications in Algebra
Volume	44
DOIs	https://doi.org/10.1080/00927872.2015.1065847
State	Published - Jan 1 2016

Disciplines

Education
Mathematics

Keywords

Gorenstein projective modules
Gorenstein ring
Left derived functor
Precover
Preenvelope
Tate homology

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https://doi.org/10.1080/00927872.2015.1065847

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title = "Gorenstein Projective Resolvents",

abstract = "Let R be a local commutative n-Gorenstein ring. The existence of the Gorenstein projective preenvelopes for finite R-modules is known (it was proved using duality arguments). In the present article, we compute an explicit Gorenstein projective preenvelope and a right Gorenstein projective resolution of a finite R-module. In light of this knowledge, we consider left derived functors Exti(−, −), (Formula presented.) , and Gexti(−, −). We prove a balance result for the Tate derived functor (Formula presented.). Finally, we get an exact sequence connecting these derived functors.",

keywords = "Gorenstein projective modules, Gorenstein ring, Left derived functor, Precover, Preenvelope, Tate homology",

author = "Edgar Enochs and Sergio Estrada and Alina Iacob and Sinem Odaba{\c s}ı",

note = "Publisher Copyright: {\textcopyright} 2016, Copyright {\textcopyright} Taylor & Francis Group, LLC.",

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doi = "10.1080/00927872.2015.1065847",

language = "American English",

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T1 - Gorenstein Projective Resolvents

AU - Enochs, Edgar

AU - Estrada, Sergio

AU - Iacob, Alina

AU - Odabaşı, Sinem

PY - 2016/1/1

Y1 - 2016/1/1

N2 - Let R be a local commutative n-Gorenstein ring. The existence of the Gorenstein projective preenvelopes for finite R-modules is known (it was proved using duality arguments). In the present article, we compute an explicit Gorenstein projective preenvelope and a right Gorenstein projective resolution of a finite R-module. In light of this knowledge, we consider left derived functors Exti(−, −), (Formula presented.) , and Gexti(−, −). We prove a balance result for the Tate derived functor (Formula presented.). Finally, we get an exact sequence connecting these derived functors.

AB - Let R be a local commutative n-Gorenstein ring. The existence of the Gorenstein projective preenvelopes for finite R-modules is known (it was proved using duality arguments). In the present article, we compute an explicit Gorenstein projective preenvelope and a right Gorenstein projective resolution of a finite R-module. In light of this knowledge, we consider left derived functors Exti(−, −), (Formula presented.) , and Gexti(−, −). We prove a balance result for the Tate derived functor (Formula presented.). Finally, we get an exact sequence connecting these derived functors.

KW - Gorenstein projective modules

KW - Gorenstein ring

KW - Left derived functor

KW - Precover

KW - Preenvelope

KW - Tate homology

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/346

UR - https://doi.org/10.1080/00927872.2015.1065847

U2 - 10.1080/00927872.2015.1065847

DO - 10.1080/00927872.2015.1065847

M3 - Article

SN - 0092-7872

VL - 44

JO - Communications in Algebra

JF - Communications in Algebra

ER -

Gorenstein Projective Resolvents

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