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 $D$

Keywords rational polynomial ring tensor product trivial extension


  • C. Faith and P. Menal. A counter example to a conjecture of Johns. (1992) @ Corollary 2.3(ii) pp 23-24
  • W. K. Nicholson and M. F. Yousif. Quasi-Frobenius Rings. (2003) @ Example 8.16, p 212

  • = has the property
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Name Measure
composition length left: $\infty$right: $\infty$

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