Persistence of homology over commutative noetherian rings

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

doi:10.1016/j.jalgebra.2022.07.027

Persistence of homology over commutative noetherian rings

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

Mathematical Sciences

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

4 Scopus citations

Abstract

We describe new classes of noetherian local rings R whose finitely generated modules M have the property that Tor_i^R(M,M)=0 for i≫0 implies that M has finite projective dimension, or Ext_Rⁱ(M,M)=0 for i≫0 implies that M has finite projective dimension or finite injective dimension.

Original language	English
Pages (from-to)	463-490
Number of pages	28
Journal	Journal of Algebra
Volume	610
DOIs	https://doi.org/10.1016/j.jalgebra.2022.07.027
State	Published - Nov 15 2022

Keywords

Finite injective dimension
Finite projective dimension
Tor

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10.1016/j.jalgebra.2022.07.027

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title = "Persistence of homology over commutative noetherian rings",

abstract = "We describe new classes of noetherian local rings R whose finitely generated modules M have the property that ToriR(M,M)=0 for i≫0 implies that M has finite projective dimension, or ExtRi(M,M)=0 for i≫0 implies that M has finite projective dimension or finite injective dimension.",

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AU - Avramov, Luchezar L.

AU - Iyengar, Srikanth B.

AU - Nasseh, Saeed

AU - Sather-Wagstaff, Keri

PY - 2022/11/15

Y1 - 2022/11/15

N2 - We describe new classes of noetherian local rings R whose finitely generated modules M have the property that ToriR(M,M)=0 for i≫0 implies that M has finite projective dimension, or ExtRi(M,M)=0 for i≫0 implies that M has finite projective dimension or finite injective dimension.

AB - We describe new classes of noetherian local rings R whose finitely generated modules M have the property that ToriR(M,M)=0 for i≫0 implies that M has finite projective dimension, or ExtRi(M,M)=0 for i≫0 implies that M has finite projective dimension or finite injective dimension.

KW - Finite injective dimension

KW - Finite projective dimension

KW - Tor

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JO - Journal of Algebra

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Persistence of homology over commutative noetherian rings

Abstract

Keywords

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