nLab associated graded ring




A filtered ring is a filtered object in the category Ring of rings.

The associated graded ring to a filtered ring is the corresponding associated graded object.


A version of PBW theorem states that if a Lie algebra gg over a field kk is flat as a kk-module over a commutative ground ring kk\supset \mathbb{Q} containing rationals, then the associated graded ring GrU(g)Gr U(g) is isomorphic to the symmetric algebra Sym(g)Sym(g) of the underlying kk-module of gg.

filtered objects

associated graded objects

Last revised on March 27, 2021 at 22:39:50. See the history of this page for a list of all contributions to it.