On modules of finite projective dimension

Research output: Contribution to journalArticle

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 nonzero divisor, if I is an ideal of finite projective dimension over R and p ∈ I or p is a nonzero divisor on R/I, then every minimal generator of I is a nonzero 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 nonzero divisor in R.

Original languageEnglish (US)
Pages (from-to)87-111
Number of pages25
JournalNagoya Mathematical Journal
Volume219
Issue number1
DOIs
Publication statusPublished - Jan 1 2015

    Fingerprint

ASJC Scopus subject areas

  • Mathematics(all)

Cite this