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 $N$
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Proc. Amer. Math. Soc. 77 (1979), 150-154 Request permission

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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