On \(SCDF\)-modules (Q6559884)

The authors obtain several properties and characterized various types of \(SCDF\)-modules. Let \(R\) be a commutative ring. An \(R\)-module \(M\) is an \(SCDF\)-module if every Dedekind finite object in \(\sigma[M]\) is finitely cogenerated. An \(R\)-module \(M\) is Dedekind finite (respectively, finitely cogenerated) if every monomorphism \(f: M \rightarrow M\) is an automorphism (respectively, if \(Soc(M)\) is essential and finitely generated). They obtain some results on local \(SCDF\)-modules, finitely generated \(SCDF\)-modules, and hollow \(SCDF\)-modules with \(Rad(M) = 0 \neq M\). They also examine \(QF\) \(SCDF\)-modules over duo-rings.