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On linear versions of some addition theorems

Abstract

Let K \subset L be a field extension. Given K-subspaces A,B of L, we study the subspace spanned by the product set AB = {ab | a \in A, b \in B}. We obtain some lower bounds on the dimension of this subspace and on dim B^n in terms of dim A, dim B and n. This is achieved by establishing linear versions of constructions and results in additive number theory mainly due to Kemperman and Olson.
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Dates and versions

hal-00258658 , version 1 (23-02-2008)

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Shalom Eliahou, Cédric Lecouvey. On linear versions of some addition theorems. 2008. ⟨hal-00258658⟩
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