##  [Nonregular Point](/nonregular-point) 

  ##  [Nonregular Point](https://algebra.quantumdictionary.io/nonregular-point-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

A point x on a scheme X whose local ring O_{X,x} is not a regular local ring; equivalently the embedding dimension (dimension of m_x/m_x^2) strictly exceeds the Krull dimension of O_{X,x}, indicating a local singularity in the sense of commutative algebra.