On \(P\)-torsion modules over a pullback of two Dedekind domains (Q2918682)

The authors consider the following setting: a pullback \(R\) of two local Dedekind domains \(R_1\) and \(R_2\), with maps \(v_1:R_1\to \overline{R}\) and \(v_2:R_2\to \overline{R}\), with maximal ideals \(P_1\) and \(P_2\), \(P=P_1\oplus P_2\) and \(R_1/P_1\cong R_2/P_2\cong R/P\cong \overline{R}\) a field. For a module \(M\) over the pullback ring \(R\) denote \(T_P(M)=\{m\in M\mid (r_1,r_2)m=0 \text{ for some } (r_1,r_2)\in R \text{ with } r_1,r_2\neq 0\}\). Then \(M\) is called \(P\)-torsion if \(T_P(M)=M\) and \(P\)-torsion-free if \(T_P(M)=0\). Among several other results on \(P\)-torsion modules, the authors classify all indecomposable \(P\)-torsion modules over a pullback of two Dedekind domains.