Draft:Idempotent ultrafilter

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{{Short description|topic in mathematics}}

{{Draft topics|europe}}

{{AfC topic|stem}}

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.