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- Title
Free resolutions over short local rings.
- Authors
Avramov, Luchezar L.; Iyengar, Srikanth B.; ͐ega, Liana M.
- Abstract
The structure of minimal free resolutions of finite modules M over commutative local rings (R, , k) with 3 = 0 and rankk(2)<rankk (/2) is studied. It is proved that over generic R every M has a Koszul syzygy module. Explicit families of Koszul modules are identified. When R is Gorenstein the non-Koszul modules are classified. Structure theorems are established for the graded k-algebra ExtR(k, k) and its graded module ExtR(M, k).
- Subjects
MATHEMATICS; MODULES (Algebra); KOSZUL algebras; LOCAL rings (Algebra); STRUCTURAL stability; FREE resolutions (Algebra)
- Publication
Journal of the London Mathematical Society, 2008, Vol 78, Issue 2, p459
- ISSN
0024-6107
- Publication type
Article
- DOI
10.1112/jlms/jdn027