On Modules of Finite Projective Dimension
Abstract
We address two aspects of finitely generated modules of finite projective dimension over local rings and their connection in between: embeddability and grade of order ideals of minimal generators of syzygies. We provide a solution of the embeddability problem and prove important reductions and special cases of the order ideal conjecture. In particular we derive that in any local ring R of mixed characteristic p > 0, where p is a non-zero-divisor, if I is an ideal of finite projective dimension over R and p is in I or p is a non-zero-divisor on R/I, then every minimal generator of I is a non-zero-divisor. Hence if P is a prime ideal of finite projective dimension in a local ring R, then every minimal generator of P is a non-zero-divisor in R.
Cite
@article{arxiv.1407.0096,
title = {On Modules of Finite Projective Dimension},
author = {Sankar P. Dutta},
journal= {arXiv preprint arXiv:1407.0096},
year = {2014}
}