On linear versions of some addition theorems

Shalom Eliahou (LMPA), C\'edric Lecouvey (LMPA)
Arxiv ID: 0802.3523Last updated: 8/19/2021
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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