HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

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.
Document type :
Journal articles
Complete list of metadata

Cited literature [18 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00618241
Contributor : Cédric Lecouvey Connect in order to contact the contributor
Submitted on : Monday, August 26, 2013 - 12:16:43 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:08 PM
Long-term archiving on: : Wednesday, November 27, 2013 - 4:21:35 AM

Files

LinearEstimatesRev2.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00618241, version 3
  • ARXIV : 1109.0134

Collections

Citation

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

Share

Metrics

Record views

98

Files downloads

160