Krull dimension of tensor products of pullbacks

2009/02/14 by Samir Bouchiba, Bouchiba, Samir
Mathematics · #13C15 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras #math.AC #msc:13C15

paper · pdf · doi:10.48550/arxiv.0902.2467

19 pages

arxiv created 2009/02/14 · openalex publication_date 2009/02/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the study of the dimension theory of tensor products of algebras over a field k. We answer an open problem set in [6] and compute dim(A⊗_kB) when A is a k-algebra arising from a specific pullback construction involving AF-domains and B is an arbitrary k-algebra. On the other hand, we deal with the question (Q) set in [5] and show, in particular, that such a pullback A is in fact a generalized AF-domain.

Related

• Dimension theory of tensor products of AF-rings
• AF-domains and their generalizations
• Local dimension theory of tensor products of algebras over a ring
• Some result on K-algebras
• Embedding dimension and codimension of tensor products of algebras over a field