# Ring detail

## Name: Simple, connected, Noetherian ring with zero divisors

This ring suggested by: JeremyRickard

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

Reference(s):

• 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

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

(Nothing was retrieved.)

(Nothing was retrieved.)