Ring $R_{ 79 }$

Cohn's non-IBN domain


$R$ 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


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

  • = 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 $\{0,1\}$
Left singular ideal $\{0\}$
Left socle $\{0\}$
Nilpotents $\{0\}$
Right singular ideal $\{0\}$
Right socle $\{0\}$
Zero divisors $\{0\}$