Description: Let $k$ be a countably infinite field and $X=\{s,t,u,v,w,x,y,z\}$ be indeterminates. Let $R$ be the free algebra over $k$ and $X$ modulo relations which make the matrix equation $AB=I_2$ hold, where $A=\begin{bmatrix}s&t\\ u&v\end{bmatrix}$ and $B=\begin{bmatrix}w&x\\ y&z\end{bmatrix}$.

Keywords free algebra quotient ring

Reference(s):

- T.-Y. Lam. Lectures on modules and rings. (2012) @ Ex 18, p 19

Symmetric properties

Asymmetric properties

Legend

- = has the property
- = does not have the property
- = information not in database

Name | Measure | |
---|---|---|

cardinality | $\aleph_0$ | |

composition length | left: $\infty$ | right: $\infty$ |

Name | Description |
---|---|

Idempotents | $\{0,1\}$ |

Nilpotents | $\{0\}$ |

Zero divisors | $\{0\}$ |