Description: $R$ is the ring 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

Reference(s):

- P. M. Cohn. Some remarks on the invariant basis property. (1966) @ pp 215-228

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 | $\{0\}$ |