TY - JOUR
T1 - Acyclicity over local rings with radical cube zero
AU - Christensen, Lars Winther
AU - Veliche, Oana
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2008
Y1 - 2008
N2 - This paper studies infinite acyclic complexes of finitely generated free modules over a commutative noetherian local ring (R, m) with m3 = 0. Conclusive results are obtained on the growth of the ranks of the modules in acyclic complexes, and new sufficient conditions are given for total acyclicity. Results are also obtained on the structure of rings that are not Gorenstein and admit acyclic complexes; part of this structure is exhibited by every ring R that admits a non-free finitely generated module M with Extn R(M, R) = 0 for a few n > 0.
AB - This paper studies infinite acyclic complexes of finitely generated free modules over a commutative noetherian local ring (R, m) with m3 = 0. Conclusive results are obtained on the growth of the ranks of the modules in acyclic complexes, and new sufficient conditions are given for total acyclicity. Results are also obtained on the structure of rings that are not Gorenstein and admit acyclic complexes; part of this structure is exhibited by every ring R that admits a non-free finitely generated module M with Extn R(M, R) = 0 for a few n > 0.
KW - Betti numbers
KW - Complete resolutions
KW - Infinite syzygies
KW - Infinite syzygy
KW - Minimal free resolutions
KW - Totally acyclic complexes
KW - Totally reflexive modules
UR - http://www.scopus.com/inward/record.url?scp=50949119991&partnerID=8YFLogxK
U2 - 10.1215/ijm/1258138553
DO - 10.1215/ijm/1258138553
M3 - Article
AN - SCOPUS:50949119991
VL - 51
SP - 1439
EP - 1454
JO - Illinois Journal of Mathematics
JF - Illinois Journal of Mathematics
SN - 0019-2082
IS - 4
ER -