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• W3038045698 abstract "We show that any finite set S in a characteristic zero integral domain can be mapped to ℤ/pℤ, for infinitely many primes p, preserving all algebraic incidences in S. This can be seen as a generalization of the well-known Freiman isomorphism lemma, which asserts that any finite subset of a torsion-free group can be mapped into ℤ/pℤ, preserving all linear incidences. As applications, we derive several combinatorial results (such as sum-product estimates) for a finite set in a characteristic zero integral domain. As ℂ is a characteristic zero integral domain, this allows us to obtain new proofs for some recent results concerning finite sets of complex numbers, without relying on the topology of the plane." @default.
• W3038045698 created "2020-07-02" @default.
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• W3038045698 date "2011-08-12" @default.
• W3038045698 modified "2023-09-23" @default.
• W3038045698 title "Mapping incidences" @default.
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• W3038045698 doi "https://doi.org/10.1112/jlms/jdr017" @default.
• W3038045698 hasPublicationYear "2011" @default.
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