Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dimension theory of tensor products of AF-rings   AF-rings are algebras over a field k which satisfy the Altitude Formula over
k. This paper surveys a few works in the literature on the Krull and valuative
dimensions of tensor products of AF-rings. The first section extends
Wadsworth's classical results on the Krull dimension of AF-domains to the
larger class of AF-rings. It also provides formulas for computing the valuative
dimension with effect on the transfer of the (locally) Jaffard property. The
second section studies tensor products of AF-rings over a zero-dimensional
ring. Most results on algebras over a field are extended to these general
constructions. The third section establishes formulas for the Krull and
valuative dimensions of tensor products of pullbacks issued from AF-domains.
Throughout, examples are provided to illustrate the scope and limits of the
results.

7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph