# Ring detail

## Name: Faith-Menal counterexample

Description: Let $D$ be a countable, existentially closed division ring over a field $F$. Let $S=D\otimes_F F(x)$. Let $R$ be the trivial extension $T(S,D)$ of $S$ by the $S$-module $D$\$

Notes:

Reference(s):

• Nicholson, W. Keith; Mohamed F. Yousif., Quasi-Frobenius Rings., Vol. 158. Cambridge University Press, (2003). Example 8.16 Pg 212

This ring has the following properties:
The ring lacks the following properties:
We don't know if the ring has or lacks the following properties: