##  [Graded Algebra](/graded-algebra) 

  ##  [Graded Algebra](https://algebra.quantumdictionary.io/graded-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 decomposed as a direct sum of homogeneous components A = ⊕_{d∈D} A_d indexed by degrees (often D = nonnegative integers or Z) such that the product maps A_i × A_j into A_{i+j}; elements are sums of homogeneous pieces.