2009/02/14 by Samir Bouchiba, Bouchiba, Samir
Chemistry · Mathematics · #13C15 #Algebraic Topology (math.AT) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Oxidative Organic Chemistry Reactions #Rings, Modules, and Algebras #math.AC #math.AT #msc:13C15
paper · pdf · doi:10.48550/arxiv.0902.2466
15 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
In this paper, we are concerned with the study of the dimension theory of tensor products of algebras over a field k. We introduce and investigate the notion of generalized AF-domain (GAF-domain for short) and prove that any k-algebra A such that the polynomial ring in one variable A[X] is an AF-domain is in fact a GAF-domain, in particular any AF-domain is a GAF-domain. Moreover, we compute the Krull dimension of A⊗kB for any k-algebra A such that A[X] is an AF-domain and any k-algebra B generalizing the main theorem of Wadsworth in [16].