# nLab filtered ring

Contents

### Context

#### Algebra

higher algebra

universal algebra

# Contents

## Definition

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.

## Examples

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