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.

To appear in Linear and Multilinear Algebra

Cited by in corpus (4)

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• Revisiting Kneser's Theorem for Field Extensions
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• Towards a function field version of Freiman's Theorem