AF-domains and their generalizations

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dc.creatorBouchiba, Samir
dc.date2009-02-14
dc.date.accessioned2026-07-07T12:42:06Z
dc.date.available2026-07-07T12:42:06Z
dc.descriptionIn 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].
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/0902.2466
dc.identifierhttp://arxiv.org/abs/0902.2466
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/219963
dc.subjectAlgebraic Topology
dc.subjectCommutative Algebra
dc.subject13C15
dc.titleAF-domains and their generalizations
dc.typetext

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