THE EVANS-GRIFFITH SYZYGY THEOREM AND BASS NUMBERS

Autor(en): BRUNS, W 
Stichwörter: COHEN-MACAULAY MODULES; Mathematics; Mathematics, Applied
Erscheinungsdatum: 1992
Herausgeber: AMER MATHEMATICAL SOC
Journal: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volumen: 115
Ausgabe: 4
Startseite: 939
Seitenende: 946
Zusammenfassung: 
Let (R, m) be a Noetherian local ring containing a field. The syzygy theorem of Evans and Griffith (see The syzygy problem, Ann. of Math. (2) 114 (1981), 323-353) says that a nonfree mth syzygy module M over R which has finite projective dimension must have rank greater-than-or-equal-to m. This theorem is an assertion about the ranks of the homomorphisms in certain acyclic complexes. It is the aim of this paper to demonstrate that the condition of acyclicity can be relaxed in a natural way. We shall use the generalization thus obtained to show that the Bass numbers of a module satisfy restrictions analogous to those which the syzygy theorem imposes on Betti numbers.
ISSN: 00029939
DOI: 10.2307/2159338

Show full item record

Page view(s)

2
Last Week
0
Last month
0
checked on Feb 26, 2024

Google ScholarTM

Check

Altmetric