A note on finite local rings (Q5905595)

Let \(R\subseteq S\) be a separable extension of finite local rings. The author shows by a counter-example, that \(S\) is not necessarily a free \(R\)-module, and so is not necessarily a Galois extension of \(R\) as it is stated by \textit{G. Ganske} and \textit{B. R. McDonald}, [Rocky Mountain J. Math. 3, 521-540 (1973; Zbl 0289.12020)]. He also explains the error in the proof in that paper.