A sum-product estimate in algebraic division algebras
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LetA be a finite subset of some normed division algebra over ℝ with cardinality ⋎A⋎. We prove that either the sum set or the product set ofA has cardinality ⋎A⋎1+δ for some δ>0.
KeywordsDivision Algebra Finite Subset Maximal Subset Additive Number Theory Normed Subspace
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