Ring $R_{ 120 }$

Cohn's right-not-left free ideal ring


Let $M$ be a monoid generated by $y$, $x_i$, $i\in \mathbb Z$ subject to the relations $yx_i=x_{i-1}$. The ring $R$ is the monoid ring $\mathbb Q[M]$.

Keywords semigroup ring


  • P. M. Cohn. Free ideal rings and localization in general rings. (2006) @ End of section 2.10, pp 174-175

  • = has the property
  • = does not have the property
  • = information not in database
Name Measure
global dimension left: right: 1
Name Description
Idempotents $\{0,1\}$
Left singular ideal $\{0\}$
Left socle $\{0\}$
Nilpotents $\{0\}$
Right singular ideal $\{0\}$
Right socle $\{0\}$
Zero divisors $\{0\}$