##  [Filtered Algebra](/filtered-algebra) 

  ##  [Filtered Algebra](https://algebra.quantumdictionary.io/filtered-algebra-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An algebra A endowed with an increasing sequence of subspaces ... = F_{-1} ⊆ F_0 ⊆ F_1 ⊆ ... whose union equals A and such that multiplication satisfies F_i · F_j ⊆ F_{i+j}; the filtration organizes elements by complexity rather than exact degree.