Nagoya Mathematical Journal
- Nagoya Math. J.
- Volume 219 (2015), 87-111.
On modules of finite projective dimension
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 of mixed characteristic , where is a nonzero divisor, if is an ideal of finite projective dimension over and or is a nonzero divisor on , then every minimal generator of is a nonzero divisor. Hence, if is a prime ideal of finite projective dimension in a local ring , then every minimal generator of is a nonzero divisor in .
Nagoya Math. J., Volume 219 (2015), 87-111.
Received: 4 March 2013
Revised: 5 March 2014
Accepted: 13 August 2014
First available in Project Euclid: 20 October 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 13D02: Syzygies, resolutions, complexes 13D22: Homological conjectures (intersection theorems)
Secondary: 13C15: Dimension theory, depth, related rings (catenary, etc.) 13D25 13H05: Regular local rings
Dutta, S. P. On modules of finite projective dimension. Nagoya Math. J. 219 (2015), 87--111. doi:10.1215/00277630-3140702. https://projecteuclid.org/euclid.nmj/1445345518