%0 Journal Article
%T A special chain theorem for the embedding dimension
%A S. Bouchiba
%A S. Kabbaj
%J Mathematics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1410.0185v1