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17 February 2025
 
  » arxiv » 1109.0134

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Pl"unnecke and Kneser type theorems for dimension estimates
Cédric Lecouvey ;
Date 1 Sep 2011
AbstractGiven 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.
Source arXiv, 1109.0134
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