The ideality conjecture for M-infinitesimals in good Bezout domains

Let $K$ be a field, let $R\subseteq K$ be a good Bezout domain, and let $I_M$ denote the set of $M$-infinitesimals. The $M$-infinitesimals $I_M$ are an ideal in $R$. This would provide the ideal-theoretic foundation for obtaining a valuation from the infinitesimals in a dp-finite field; the supplied context does not state whether the claim is known or remains open.