##  [Tensor Algebra](/tensor-algebra) 

  ##  [Tensor Algebra](https://algebra.quantumdictionary.io/tensor-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

The free associative unital algebra generated by a module or vector space V, constructed as the direct sum of all tensor powers T(V)=k ⊕ V ⊕ V⊗V ⊕ V⊗V⊗V ⊕ ··· with multiplication given by tensor concatenation.