On secondary modules over Dedekind domains (Q5943056)

Let \(R\) be a commutative ring. An \(R\)-module \(M\) is secondary if left multiplication by an element of \(R\) is either a surjective or a nilpotent endomorphism of \(M\). The author classifies such modules when \(R\) is local and Dedekind. NEWLINENEWLINENEWLINELet \(P\) be the maximal ideal of \(R\). The three types of indecomposable secondary modules are (i) \(R/P^n\); (ii) the injective hull of \(R/P\); (iii) the field of fractions of \(R\).