We further investigate a divisibility relation on the set $\beta \mathbb{N}$ of ultrafilters on the set of natural numbers. We single out prime ultrafilters (divisible only by 1 and themselves) and establish a hierarchy in which a position of every ultrafilter depends on the set of prime ultrafilters it is divisible by. We also construct ultrafilters with many immediate successors in this hierarchy and find positions of products of ultrafilters.

中文翻译：

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$\stackrel{〜}{|}$超滤器的可除性

我们进一步研究集合上的除数关系 $\beta \mathbb{ñ}$一组自然数上的超滤器。我们挑选素数超滤器（只能被1及其自身整除），并建立一个层次结构，其中每个超滤器的位置都取决于素数超滤器可被其整除的集合。我们还在此层次结构中构建了具有许多直接后继产品的超滤器，并找到了超滤器产品的位置。