On a class of rings with essential right socle (Q1823299)

A subset \(0\not\in L\subseteq M\) of a right \(A\)-module \(M\) is said to be a set of cogenerators of \(M\) if \(L\cap N\neq \emptyset\) for every non-zero submodule \(N\) of \(M\). The authors characterize modules possessing a finite set of cogenerators. This yields also a characterization of the class of rings having the property that the class of finitely cogenerated modules and that of modules with finite set of cogenerators coincide.