Let $k$ be a countably infinite field. Let $S$ be the power series ring over $k$ in two noncommuting variables $x,y$. The ring is $R=S/(y^2,yx)$
Keywords power series ring quotient ring
| Name | Measure | |
|---|---|---|
| cardinality | $\mathfrak c$ | |
| composition length | left: $\infty$ | right: $\infty$ |
| Name | Description |
|---|---|
| Idempotents | $\{0,1\}$ |
| Jacobson radical | $J(R)=(x,y)$ |
| Left socle | $\{0\}$ |