Ring $R_{ 121 }$

Simple, Noetherian ring with zero divisors and trivial idempotents


Let $k$ be a field of characteristic $2$, and $\lambda\in k$ be a (nonzero) element that isn't a root of unity. $R=k\langle x, x^{-1}, y, y^{-1}\rangle/\langle xy-\lambda yx\rangle$.

Keywords free algebra quotient ring twisted group ring


  • A. Zalesskii and O. Neroslavskii. There exist simple Noetherian rings with zero divisors but without idempotents. (1977) @ (main result)
  • M. Lorenz. K0 of skew group rings and simple noetherian rings without idempotents. (1985) @ Example 1.8 p 46

  • = has the property
  • = does not have the property
  • = information not in database

(Nothing was retrieved.)

Name Description
Idempotents $\{0,1\}$
Jacobson radical $\{0\}$
Left singular ideal $\{0\}$
Right singular ideal $\{0\}$