Definition:Filtered Algebra
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Definition
A filtered algebra is a generalization of the notion of a graded algebra.
A filtered algebra over the field $k$ is an algebra $\struct {A_k, \oplus}$ over $k$ which has an increasing sequence $\set 0 \subset F_0 \subset F_1 \subset \cdots \subset F_i \subset \cdots \subset A$ of substructures of $A$ such that:
- $\ds A = \bigcup_{i \mathop \in \N} F_i$
and that is compatible with the multiplication in the following sense:
- $\forall m, n \in \N: F_m \cdot F_n \subset F_{n + m}$
Also see
- Results about filtered algebras can be found here.
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