# Commutative ring detail

## Name: Complex numbers: $\mathbb C$

Description: With real numbers $\mathbb R$, $\mathbb R[x]/(x^2+1)$ OR the set of real matrices of form $\left[\begin{smallmatrix}a&b\\-b&a\end{smallmatrix}\right]$ with determinant greater than $0$. OR the real Clifford algebra for signature (-)

Notes:

Keywords quotient ring subring matrix ring

Reference(s):

• (Citation needed)

• This ring has the following properties:
The ring lacks the following properties:
We don't know if the ring has or lacks the following properties: