TY - JOUR
T1 - Totally acyclic complexes and locally Gorenstein rings
AU - Christensen, Lars Winther
AU - Kato, Kiriko
N1 - Publisher Copyright:
© 2018 World Scientific Publishing Company.
PY - 2018/3/1
Y1 - 2018/3/1
N2 - A commutative noetherian ring with a dualizing complex is Gorenstein if and only if every acyclic complex of injective modules is totally acyclic. We extend this characterization, which is due to Iyengar and Krause, to arbitrary commutative noetherian rings, i.e. we remove the assumption about a dualizing complex. In this context Gorenstein, of course, means locally Gorenstein at every prime.
AB - A commutative noetherian ring with a dualizing complex is Gorenstein if and only if every acyclic complex of injective modules is totally acyclic. We extend this characterization, which is due to Iyengar and Krause, to arbitrary commutative noetherian rings, i.e. we remove the assumption about a dualizing complex. In this context Gorenstein, of course, means locally Gorenstein at every prime.
KW - Gorenstein ring
KW - totally acyclic complex
UR - http://www.scopus.com/inward/record.url?scp=85030850017&partnerID=8YFLogxK
U2 - 10.1142/S0219498818500391
DO - 10.1142/S0219498818500391
M3 - Article
AN - SCOPUS:85030850017
SN - 0219-4988
VL - 17
JO - Journal of Algebra and its Applications
JF - Journal of Algebra and its Applications
IS - 3
M1 - 1850039
ER -