Noncommutative resolutions using syzygies: NONCOMMUTATIVE RESOLUTIONS USING SYZYGIES
- Award ID(s):
- 1503044
- PAR ID:
- 10078231
- Publisher / Repository:
- Oxford University Press (OUP)
- Date Published:
- Journal Name:
- Bulletin of the London Mathematical Society
- Volume:
- 51
- Issue:
- 1
- ISSN:
- 0024-6093
- Page Range / eLocation ID:
- p. 43-48
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract The Burch index is a new invariant of a local ringRwhose positivity implies a kind of linearity in resolutions ofR-modules. We show that ifRhas depth zero and Burch index at least 2, then any non-free 7thR-syzygy contains the residue field as a direct summand. We compute the Burch index in various cases of interest.more » « less