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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Ramsey theory in noncommutative semigroups


Authors: Vitaly Bergelson and Neil Hindman
Journal: Trans. Amer. Math. Soc. 330 (1992), 433-446
MSC: Primary 03E05; Secondary 05D10, 22A15, 54H15, 54H20
MathSciNet review: 1069744
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Abstract: By utilizing ultrafilters we give a general version of the Central Sets Theorem [$ 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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1069744-5
PII: S 0002-9947(1992)1069744-5
Keywords: Ramsey theory, noncommutative semigroups, van der Waerden's Theorem
Article copyright: © Copyright 1992 American Mathematical Society