Результаты поиска по запросу «natural logarithm»

A complete local ring with a finitely generated maximal ideal is Noetherian. Drop completeness and it fails: an ultraproduct construction gives a non-Noetherian local ring whose maximal ideal is principal.

Why the definition of a filtered category insists on non-emptiness: the empty colimit fails to commute with the empty limit, and that is the only failure.