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Simultaneous idempotents in $ \beta \mathbf{N}_{\mathbf{N}}$ and finite sums and products in $ N$


Author: Neil Hindman
Journal: Proc. Amer. Math. Soc. 77 (1979), 150-154
MSC: Primary 05A17; Secondary 10A45, 54D40
DOI: https://doi.org/10.1090/S0002-9939-1979-0539649-3
MathSciNet review: 539649
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Abstract: The principal result is that there do not exist simultaneous multiplicative and additive idempotents in $ \beta N\backslash N$. Some consequences of the (already known) existence of multiplicative idempotents which are close to additive idempotents are also derived.


References [Enhancements On Off] (What's this?)

  • [1] J. Baumgartner, A short proof of Hindman's Theorem, J. Combinatoral Theory Ser. A 17 (1974), 384-386. MR 0354394 (50:6873)
  • [2] W. W. Comfort, Ultrafilters: some old and some new results, Bull. Amer. Math. Soc. 83 (1977), 417-455. MR 0454893 (56:13136)
  • [3] E. van Douwen, Extensions on binary operations on $ \beta \omega $ (preprint).
  • [4] H. Furstenberg and B. Weiss, Topological dynamics and combinatorial number theory, J. Analyse Math. (to appear). MR 531271 (80g:05009)
  • [5] S. Glazer, Ultrafilters and semigroup combinatorics, J. Combinatoral Theory Ser. A (to appear).
  • [6] R. Graham and B. Rothschild, Ramsey's Theorem for n-parameter sets, Trans. Amer. Math. Soc. 159 (1971), 257-292. MR 0284352 (44:1580)
  • [7] N. Hindman, Finite sums from sequences within cells of a partition of N, J. Combinatoral Theory Ser. A 17 (1974), 1-11. MR 0349574 (50:2067)
  • [8] -, Partitions and sums and products of integers, Trans. Amer. Math. Soc. 247 (1979), 227-245. MR 517693 (80b:10022)
  • [9] -, The existence of certain ultrafilters on N and a conjecture of Graham and Rothschild, Proc. Amer. Math. Soc. 36 (1972), 341-346. MR 0307926 (46:7041)
  • [10] J. Sanders, A generalization of Schur's theorem, Thesis, Yale University, 1968.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0539649-3
Keywords: Idempotents, ultrafilters, partitions
Article copyright: © Copyright 1979 American Mathematical Society

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