A remark on power series rings (Q1802370)

The main result of this short note is a trivializability principle for a class of local rings. More precisely, let \(R\) be a local semihereditary ring with maximal ideal \(\mathcal M\) and suppose that \(\mathcal M\) is finitely generated as right ideal. The author proves then that \(R\) satisfies the inverse weak algorithm relatively to the \(\mathcal M\)-adic filtration iff \(\bigcap{\mathcal M}^ n=0\).