# Ring detail

## Name: Michler & Villemayor's right-not-left V ring

Description: Let $V$ be an infinite dimensional right vector space over a countably infinite field $k$. Let $T$ be the ring of linear transformations $V\to V$. Let $S$ be the socle of $T$. The ring $R$ is the subring of $T$ generated by $S$ and the center of $T$.

Keywords infinite matrix ring subring

Reference(s):

• G. O. Michler and O. Villamayor. On rings whose simple modules are injective. (1973) @ Remark 4.5 pp 192-193

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 $\{0\}$