Noetherian rings of low global dimension and syzygetic prime ideals
Commutative Algebra
2019-10-04 v1
Abstract
Let be a Noetherian ring. We prove that has global dimension at most two if, and only if, every prime ideal of is of linear type. Similarly, we show that has global dimension at most three if, and only if, every prime ideal of is syzygetic. As a consequence, one derives a characterization of these rings using the Andr\'e-Quillen homology.
Keywords
Cite
@article{arxiv.1910.01550,
title = {Noetherian rings of low global dimension and syzygetic prime ideals},
author = {Francesc Planas-Vilanova},
journal= {arXiv preprint arXiv:1910.01550},
year = {2019}
}