Embedding dimension and codimension of tensor products of algebras over a field

2017/01/19 by S. Bouchiba, Bouchiba, S., S. Kabbaj +1
Mathematics · #13B30 #13D05 #13E05 #13F20 #13H05 #14M05 #16E65 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1701.05365

openalex publication_date 2017/01/19 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

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.

Related

• Local dimension theory of tensor products of algebras over a ring
• A special chain theorem for the embedding dimension
• Some result on K-algebras
• Cohen-Macaulay, Gorenstein, Complete intersection and regular defect for the tensor product of algebras
• Krull dimension of tensor products of pullbacks