Ring $R_{ 42 }$

Local right-not-left Kasch ring


Let $k$ be a countably infinite field. Let $S$ be the power series ring over $k$ in two noncommuting variables $x,y$. The ring is $R=S/(y^2,yx)$

Keywords power series ring quotient ring


  • T.-Y. Lam. Exercises in modules and rings. (2007) @ ex 3.18, p 211

  • = has the property
  • = does not have the property
  • = information not in database
Name Measure
cardinality $\mathfrak c$
composition length left: $\infty$right: $\infty$
Name Description
Idempotents $\{0,1\}$
Jacobson radical $J(R)=(x,y)$
Left socle $\{0\}$