Commutative rings whose proper ideals are \(\wp\)-virtually semisimple (Q2682707)

Throughout this paper, all rings \(R\) are commutative and associative with identity and, all modules \(M\) are unital. An \(R\)-module \(M\) is called virtually semisimple (respectively, virtually simple) if each submodule of \(M\) is isomorphic to a direct summand of \(M\) (respectively, if \(M\not= (0)\) and \(N \cong M\) holds true for every non-zero submodule \(N\) of \(M\)). In this paper, the authors study commutative rings \(R\) whose proper (prime) ideals are direct sums of virtually simple \(R\)-modules. This is a continuation of \textit{M. Behboodi} and \textit{E. Bigdeli} [Commun. Algebra 47, No. 10, 3995--4008 (2019; Zbl 1434.16004)].