Module-theoretic characterizations of Krull domains (Q2890353)

Let \(R\) be an infra-Krull domain. The aim of the paper is to show that the following are equivalent: (1) \(R\) is a Krull domain; (2) For any essentially finite \(w\)-module \(M\) over \(R\), the torsion submodule \(t(M)\) is a direct summand of \(M\); (3) For any essentially finite \(w\)-module \(M\) over \(R\), \(t(M)\cap pM=pt(M)\) for any maximal \(w\)-ideal \(p\) of \(R\); (4) \(R\) satisfies the \(w\)-radical formula; (5) The \(R\)-module \(R\oplus R\) satisfies the \(w\)-radical formula.