Ring $R_{ 58 }$

Simple, non-Artinian, von Neumann regular ring


Let $T=R_{15}$ be the ring of linear transformations of a countable dimensional vector space over $\mathbb Q$. This is known to have exactly one nontrivial ideal $S$. The required ring is $R=T/S$


  • (Citation needed)

  • Legend
    • = has the property
    • = does not have the property
    • = information not in database
    Name Measure
    composition length left: $\infty$right: $\infty$
    weak global dimension 0
    Name Description
    Jacobson radical $\{0\}$
    Left singular ideal $\{0\}$
    Left socle $\{0\}$
    Right singular ideal $\{0\}$
    Right socle $\{0\}$