Title

Eventually Linear Partially Complete Resolutions Over a Local Ring with m4=0

Status

Faculty

School

School of Science

Department

Math/Computer Science

Document Type

Article

Publication Date

4-2016

Publication Title

Journal of Algebra and its Applications

Description/Abstract

We classify the Hilbert polynomial of a local ring (R,m)(R,𝔪) satisfying m4=0𝔪4=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=0𝔪4=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=0𝔪4=0 local ring cannot be periodic of period two or three.

Keywords

Linear resolution, complete resolution, totally reflexive module, Hilbert series

Volume

15

Issue

3

Scholarly

yes

DOI

10.1142/S0219498816500559

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

This document is currently not available here.

Share

COinS