Mathematics – Algebraic Topology
Scientific paper
2009-02-14
Mathematics
Algebraic Topology
15 pages
Scientific paper
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 $A\otimes_kB$ 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].
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