Embedding dimension and codimension of tensor products of algebras over a field
Commutative Algebra
2017-01-20 v1
Abstract
Let k be a field. This paper investigates the embedding dimension and codimension of Noetherian local rings arising as localizations of tensor products of k-algebras. We use results and techniques from prime spectra and dimension theory to establish an analogue of the "special chain theorem" for the embedding dimension of tensor products, with effective consequence on the transfer or defect of regularity as exhibited by the (embedding) codimension.
Keywords
Cite
@article{arxiv.1701.05365,
title = {Embedding dimension and codimension of tensor products of algebras over a field},
author = {S. Bouchiba and S. Kabbaj},
journal= {arXiv preprint arXiv:1701.05365},
year = {2017}
}
Comments
To appear in: Rings, Polynomials, and Modules, Springer, New York, pp. 1-25