Homology Over Trivial Extensions of Commutative DG Algebras

Luchezar L. Avramov; Srikanth B. Iyengar; Saeed Nasseh; Sean Sather-Wagstaff

Homology Over Trivial Extensions of Commutative DG Algebras

Luchezar L. Avramov
, Srikanth B. Iyengar
, Saeed Nasseh
, Sean Sather-Wagstaff

Mathematical Sciences

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

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Abstract

Conditions on the Koszul complex of a noetherian local ring R guarantee that TorRi(M,N) is non-zero for infinitely many i, when M and N are finitely generated R-modules of infinite projective dimension. These conditions are obtained from results concerning Tor of differential graded modules over certain trivial extensions of commutative differential graded algebras.

Original language	American English
Journal	arXIV.org Repository
State	Published - Aug 4 2015

Disciplines

Education
Mathematics

Keywords

Commutative DG algebras
Homology
Trivial extensions

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title = "Homology Over Trivial Extensions of Commutative DG Algebras",

abstract = " Conditions on the Koszul complex of a noetherian local ring R guarantee that TorRi(M,N) is non-zero for infinitely many i, when M and N are finitely generated R-modules of infinite projective dimension. These conditions are obtained from results concerning Tor of differential graded modules over certain trivial extensions of commutative differential graded algebras.",

keywords = "Commutative DG algebras, Homology, Trivial extensions",

author = "Avramov, \{Luchezar L.\} and Iyengar, \{Srikanth B.\} and Saeed Nasseh and Sean Sather-Wagstaff",

year = "2015",

month = aug,

day = "4",

language = "American English",

journal = "arXIV.org Repository",

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TY - JOUR

T1 - Homology Over Trivial Extensions of Commutative DG Algebras

AU - Avramov, Luchezar L.

AU - Iyengar, Srikanth B.

AU - Nasseh, Saeed

AU - Sather-Wagstaff, Sean

PY - 2015/8/4

Y1 - 2015/8/4

N2 - Conditions on the Koszul complex of a noetherian local ring R guarantee that TorRi(M,N) is non-zero for infinitely many i, when M and N are finitely generated R-modules of infinite projective dimension. These conditions are obtained from results concerning Tor of differential graded modules over certain trivial extensions of commutative differential graded algebras.

AB - Conditions on the Koszul complex of a noetherian local ring R guarantee that TorRi(M,N) is non-zero for infinitely many i, when M and N are finitely generated R-modules of infinite projective dimension. These conditions are obtained from results concerning Tor of differential graded modules over certain trivial extensions of commutative differential graded algebras.

KW - Commutative DG algebras

KW - Homology

KW - Trivial extensions

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/416

M3 - Article

JO - arXIV.org Repository

JF - arXIV.org Repository

ER -

Homology Over Trivial Extensions of Commutative DG Algebras

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