##  [Power Series Ring](/power-series-ring) 

  ##  [Power Series Ring](https://algebra.quantumdictionary.io/power-series-ring-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 ring consisting of formal sums ∑_{α} c_{α} x^{α} in one or more indeterminates x with coefficients c_{α} in a given coefficient ring or field, where infinite sums are allowed but no analytic convergence is required; addition and multiplication are defined termwise and by the Cauchy product.