Simultaneous idempotents in 𝛽𝐍_{𝐍} and finite sums and products in 𝐍

Hindman, Neil

doi:10.1090/S0002-9939-1979-0539649-3

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

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

[1] James E. Baumgartner, A short proof of Hindman’s theorem, J. Combinatorial Theory Ser. A 17 (1974), 384–386. MR 0354394
[2] W. W. Comfort, Ultrafilters: some old and some new results, Bull. Amer. Math. Soc. 83 (1977), no. 4, 417–455. MR 0454893, https://doi.org/10.1090/S0002-9904-1977-14316-4
[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. 34 (1978), 61–85 (1979). MR 531271, https://doi.org/10.1007/BF02790008
[5] S. Glazer, Ultrafilters and semigroup combinatorics, J. Combinatoral Theory Ser. A (to appear).
[6] R. L. Graham and B. L. Rothschild, Ramsey’s theorem for 𝑛-parameter sets, Trans. Amer. Math. Soc. 159 (1971), 257–292. MR 0284352, https://doi.org/10.1090/S0002-9947-1971-0284352-8
[7] Neil Hindman, Finite sums from sequences within cells of a partition of 𝑁, J. Combinatorial Theory Ser. A 17 (1974), 1–11. MR 0349574
[8] Neil Hindman, Partitions and sums and products of integers, Trans. Amer. Math. Soc. 247 (1979), 227–245. MR 517693, https://doi.org/10.1090/S0002-9947-1979-0517693-4
[9] Neil Hindman, The existence of certain ultra-filters on 𝑁 and a conjecture of Graham and Rothschild, Proc. Amer. Math. Soc. 36 (1972), 341–346. MR 0307926, https://doi.org/10.1090/S0002-9939-1972-0307926-0
[10] J. Sanders, A generalization of Schur's theorem, Thesis, Yale University, 1968.

Bibliography