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Plünnecke and Kneser type theorems for dimension estimates

Abstract : 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 Plünnecke 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 Plünnecke 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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https://hal.archives-ouvertes.fr/hal-00618241
Contributor : Cédric Lecouvey <>
Submitted on : Monday, August 26, 2013 - 12:16:43 PM
Last modification on : Wednesday, August 29, 2018 - 1:09:08 AM
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  • HAL Id : hal-00618241, version 3
  • ARXIV : 1109.0134

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Cédric Lecouvey. Plünnecke and Kneser type theorems for dimension estimates. Combinatorica, Springer Verlag, 2014. ⟨hal-00618241v3⟩

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