Combinatorial Nullstellensatz over division rings

Research output: Contribution to journalArticlepeer-review


We extend Alon’s Combinatorial Nullstellensatz from polynomial rings over fields to polynomial rings over division rings and to rings of polynomial functions over centrally finite division algebras. We apply our results to extend classical theorems from additive number theory to the additive theory of division rings, where the size of algebraic sets is measured by their rank in the sense of Lam.

Original languageEnglish
Pages (from-to)895-911
Number of pages17
JournalJournal of Algebraic Combinatorics
Issue number3
StatePublished - Nov 2023


  • Combinatorial Nullstellensatz
  • Division rings
  • Noncommutative ring theory

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics


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