Eventually Linear Partially Complete Resolutions Over a Local Ring with m4=0
SMC Affiliated Work
1
Status
Faculty
School
School of Science
Department
Math/Computer Science
Document Type
Article
Publication Date
4-2016
Publication / Conference / Sponsorship
Journal of Algebra and its Applications
Description/Abstract
We classify the Hilbert polynomial of a local ring (R,m)(R,�) satisfying m4=0�4=0 which admits a doubly-infinite eventually linear resolution CC which is “partially” complete — that is, for which HiHomR(C,R)HiHomR(C,R) vanishes for all |i|≫0|i|≫0. As a corollary to our main result, we show that an m4=0�4=0 local ring can admit certain classes of asymmetric partially complete resolutions only if its Hilbert polynomial is symmetric. Moreover, we show that the Betti sequence associated to an eventually linear partially complete resolution over an m4=0�4=0 local ring cannot be periodic of period two or three.
Keywords
Linear resolution, complete resolution, totally reflexive module, Hilbert series
Scholarly
yes
DOI
10.1142/S0219498816500559
Volume
15
Issue
3
Disciplines
Mathematics
Original Citation
Kristen Beck (Mathematics and Computer Science): “Eventually linear partially complete resolutions over a local ring with m4=0,” Kristen A. Beck, in the Journal of Algebra and its Applications, Vol. 15, No. 03, April 2016. Doi:10.1142/S0219498816500559. http://www.worldscientific.com/doi/abs/10.1142/S0219498816500559
Repository Citation
Beck, Kristen. Eventually Linear Partially Complete Resolutions Over a Local Ring with m4=0 (2016). Journal of Algebra and its Applications. 15 (3), 10.1142/S0219498816500559 [article]. https://digitalcommons.stmarys-ca.edu/school-science-faculty-works/7
