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associated graded ring

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Definition

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.

Properties

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.

Revised on October 18, 2012 19:37:43 by Zoran Škoda (161.53.130.104)