Draft:Idempotent ultrafilter

Submission declined on 1 January 2025 by KylieTastic (talk).

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Declined by KylieTastic 2 seconds ago. Last edited by KylieTastic 2 seconds ago. Reviewer: Inform author.

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An idempotent ultrafilter on a semigroup S is an ultrafilter which is an idempotent in the semigroup of ultrafilters on S taken with the convolution operation. The existence of an idempotent ultrafilter on any semigroup follows from the Ellis-Numakura lemma and its proof depends on Zorn's lemma.

The notion of an IP set is connected with idempotent ultrafilters.

References

Todorcevic, Stevo. "Introduction to Ramsey spaces" Annals of Mathematics Studies 174. (2010): 1-296.