# Ring detail

## Name: Cohn's non-IBN domain

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 $n=3$.

Krull dimension: (unknown)

Keywords free algebra quotient ring

Reference(s):

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