Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pl\"unnecke and Kneser type theorems for dimension estimates   Given a division ring K containing the field k in its center and A,B two
finite subsets of K\{0}, we give some analogues of Pl\"unnecke and Kneser
theorems for the dimension of the k-linear span of the Minkowski product AB in
terms of the dimensions of the k-linear spans of A and B. These Pl\"unnecke
type estimates are then generalized to the case of associative algebras. We
also obtain an analogue in the context of division rings of a theorem by Tao
classifying the sets of small doubling in a group.

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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg