Hindmanʼs coloring theorem in arbitrary semigroups

@article{Golan2013HindmansCT,
  title={Hindmanʼs coloring theorem in arbitrary semigroups},
  author={Gili Golan and B. Tsaban},
  journal={Journal of Algebra},
  year={2013},
  volume={395},
  pages={111-120}
}
Abstract Hindmanʼs Theorem asserts that, for each finite coloring of the natural numbers, there are distinct natural numbers a 1 , a 2 , … such that all of the sums a i 1 + a i 2 + ⋯ + a i m ( m ⩾ 1 , i 1 i 2 ⋯ i m ) have the same color. The celebrated Galvin–Glazer proof of Hindmanʼs Theorem and a classification of semigroups due to Shevrin, imply together that, for each finite coloring of each infinite semigroup S, there are distinct elements a 1 , a 2 , … of S such that all but finitely many… Expand
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