nLab filtered ring




A filtered ring (resp. filtered algebra) is a monoid object in the category of filtered abelian groups (resp. filtered vector spaces).

One considers positive and negative filtrations, as well as \mathbb{Z}-filtrations.

To-do list: complete filtrations, associated graded ring, symbol map, Poisson structure on the associated graded algebra if the latter is commutative.


A major example is the universal enveloping algebra of any Lie algebra.

See also Lazard's criterion and microlocalization.

filtered objects

associated graded objects


Last revised on November 25, 2019 at 14:33:26. See the history of this page for a list of all contributions to it.