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Journal of the London Mathematical Society Advance Access originally published online on July 8, 2008
Journal of the London Mathematical Society 2008 78(2):459-476; doi:10.1112/jlms/jdn027
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© 2008 London Mathematical Society

Free resolutions over short local rings

Luchezar L. Avramov and Srikanth B. Iyengar

Department of Mathematics
University of Nebraska
Lincoln, NE 68588
USA
avramov@math.unl.edu

Liana M. Sega

Department of Mathematics and Statistics
University of Missouri
Kansas City, MO 64110
USA
segal@umkc.edu

The structure of minimal free resolutions of finite modules M over commutative local rings (R, m, k) with m3 = 0 and rankk(m2)<rankk (m/m2) 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).

2000 Mathematics Subject Classification 13D02 (primary), 13D07 (secondary).

To the memory of our friend and colleague Anders Frankild

The research was partly supported by NSF grants DMS 0201904 (LLA) and DMS 0602498 (SBI).

Received July 30, 2007; revised February 26, 2008; published online July 8, 2008.


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