A special chain theorem for the embedding dimension
Commutative Algebra
2017-01-23 v2
Abstract
This paper establishes an analogue of the special chain theorem for the embedding dimension of polynomial rings, with direct application on the (embedding) codimension. In particular, we recover a classic result on the transfer of regularity to polynomial rings (initially proved via a combination of Serre's result on finite global dimension and Hilbert theorem on syzygies). A second application characterizes regularity in general settings of localizations of polynomial rings, including Nagata rings and Serre's conjecture rings.
Cite
@article{arxiv.1410.0185,
title = {A special chain theorem for the embedding dimension},
author = {S. Bouchiba and S. Kabbaj},
journal= {arXiv preprint arXiv:1410.0185},
year = {2017}
}
Comments
This manuscript has been withdrawn by the author since it was included as a section within another paper entitled "Embedding dimension and codimension of tensor products of algebras over a field" arXiv:1701.05365