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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0539649-3
PII: S 0002-9939(1979)0539649-3
Keywords: Idempotents, ultrafilters, partitions
Article copyright: © Copyright 1979 American Mathematical Society