Topology Proceedings
Document # baak-18
Electronic Version 24 Summer (1999) |
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Weak VIP Systems in Commutative Semigroups
Neil Hindman and Randall McCutcheon
Let (G,+) be a (discrete) commutative semigroup. VIP systems in G are polynomial type generalizations of IP systems, (i.e., sets of finite sums). We provide a self contained algebraic proof, using the algebraic structure of the Stone- Cech compactification \betaG of G, of a partition theorem about finite sets of VIP systems in abelian groups which had been previously derived as a consequence of the Polynomial Hales-Jewett Theorem due to V. Bergelson and A. Leibman. We also establish an infinitary version of this result valid in arbitrary commutative semigroups.
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Date published electronically: March 5, 2001.