TY - JOUR

T1 - Growth in the minimal injective resolution of a local ring

AU - Christensen, Lars Winther

AU - Striuli, Janet

AU - Veliche, Oana

N1 - Funding Information:
This work started while the first author visited the University of Nebraska-Lincoln, partly supported by a grant from the Carlsberg Foundation. The second author was supported by NSF grant DMS 0201904.

PY - 2010/2

Y1 - 2010/2

N2 - Let R be a commutative noetherian local ring with residue field k and assume that it is not Gorenstein. In the minimal injective resolution of R, the injective envelope E of the residue field appears as a summand in every degree starting from the depth of R. The number of copies of E in degree i equals the k-vector space dimension of the cohomology module ExtiR(k, R). These dimensions, known as Bass numbers, form an infinite sequence of invariants of R about which little is known. We prove that it is non-decreasing and grows exponentially if R is Golod, a non-trivial fiber product, or Teter, or if it has radical cube zero.

AB - Let R be a commutative noetherian local ring with residue field k and assume that it is not Gorenstein. In the minimal injective resolution of R, the injective envelope E of the residue field appears as a summand in every degree starting from the depth of R. The number of copies of E in degree i equals the k-vector space dimension of the cohomology module ExtiR(k, R). These dimensions, known as Bass numbers, form an infinite sequence of invariants of R about which little is known. We prove that it is non-decreasing and grows exponentially if R is Golod, a non-trivial fiber product, or Teter, or if it has radical cube zero.

UR - http://www.scopus.com/inward/record.url?scp=76549114689&partnerID=8YFLogxK

U2 - 10.1112/jlms/jdp058

DO - 10.1112/jlms/jdp058

M3 - Article

AN - SCOPUS:76549114689

SN - 0024-6107

VL - 81

SP - 24

EP - 44

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 1

ER -