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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
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?)

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Keywords: Idempotents, ultrafilters, partitions
Article copyright: © Copyright 1979 American Mathematical Society

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