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Article overview
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Pl"unnecke and Kneser type theorems for dimension estimates | Cédric Lecouvey
; | Date: |
1 Sep 2011 | 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 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 | Services: | Forum | Review | PDF | Favorites |
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