$R$ is the free $\mathbb Z$ algebra with generators $\{a_{ij}, b_{kl}\mid 1\leq i,l\leq 2, 1\leq j, k\leq 3\}$, satisfying the relations $(a_{ij})(b_{kl})=I_2$ and $(b_{kl})(a_{ij})=I_3$
Notes: Special case of a more general construction with $m=2$ and $n=3$.
Keywords free algebra quotient ring
| Name | Measure | |
|---|---|---|
| cardinality | $\aleph_0$ | |
| composition length | left: $\infty$ | right: $\infty$ |
| Name | Description |
|---|---|
| Idempotents | $\{0,1\}$ |
| Left singular ideal | $\{0\}$ |
| Left socle | $\{0\}$ |
| Nilpotents | $\{0\}$ |
| Right singular ideal | $\{0\}$ |
| Right socle | $\{0\}$ |
| Zero divisors | $\{0\}$ |