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September 2015 On modules of finite projective dimension
S. P. Dutta
Nagoya Math. J. 219: 87-111 (September 2015). DOI: 10.1215/00277630-3140702

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 pI 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.

Citation

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S. P. Dutta. "On modules of finite projective dimension." Nagoya Math. J. 219 87 - 111, September 2015. https://doi.org/10.1215/00277630-3140702

Information

Received: 4 March 2013; Revised: 5 March 2014; Accepted: 13 August 2014; Published: September 2015
First available in Project Euclid: 20 October 2015

zbMATH: 1007.13006
MathSciNet: MR3413574
Digital Object Identifier: 10.1215/00277630-3140702

Subjects:
Primary: 13D02, 13D22
Secondary: 13C15, 13D25, 13H05

Rights: Copyright © 2015 Editorial Board, Nagoya Mathematical Journal

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Vol.219 • September 2015
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