# 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 $D$\$

Krull dimension: (unknown)

Reference(s):

• W. K. Nicholson and M. F. Yousif. Quasi-Frobenius Rings. (2003) @ Example 8.16, p 212