Ramsey Theory in Noncommutative Semigroups

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1992Publisher:JSTORJournal:Transactions of the American Mathematical Society, volume 330, page 433 (issn: 0002-9947,

Copyright policy )Funded by:NSF | Mathematical Sciences: Co..., NSF | Mathematical Sciences: Mu...

Authors: Bergelson, Vitaly; Hindman, Neil;

doi: 10.2307/2154173 , 10.1090/s0002-9947-1992-1069744-5

Ramsey Theory in Noncommutative Semigroups

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Abstract

By utilizing ultrafilters we give a general version of the Central Sets Theorem [ 6 6 , Proposition 8.21]. This enables us to derive noncommutative versions of van der Waerden’s Theorem and several of its generalizations. We also derive some standard results, including the Hales-Jewett Theorem.

Related Organizations

Howard University
United States
THE OHIO STATE UNIVERSITY
United States

Keywords

van der Waerden's theorem, Combinatorial aspects of partitions of integers, Ramsey theory, Structure of topological semigroups, noncommutative semigroups, Hales-Jewett theorem

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