Soydan, I.; Türkmen, E. Generalizations of \(ss\)-supplemented modules. (English) Zbl 1496.16001 Carpathian Math. Publ. 13, No. 1, 119-126 (2021). Summary: We introduce the concept of (strongly) \(ss\)-radical supplemented modules. We prove that if a submodule \(N\) of \(M\) is strongly \(ss\)-radical supplemented and \(Rad(M/N)=M/N\), then \(M\) is strongly \(ss\)-radical supplemented. For a left good ring \(R\), we show that \(Rad(R)\subseteq Soc(_RR)\) if and only if every left \(R\)-module is \(ss\)-radical supplemented. We characterize the rings over which all modules are strongly \(ss\)-radical supplemented. We also prove that over a left \(WV\)-ring every supplemented module is \(ss\)-supplemented. MSC: 16D10 General module theory in associative algebras 16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras Keywords:semisimple module; (strongly) \(ss\)-radical supplemented module; \(WV\)-rings PDFBibTeX XMLCite \textit{I. Soydan} and \textit{E. Türkmen}, Carpathian Math. Publ. 13, No. 1, 119--126 (2021; Zbl 1496.16001) Full Text: DOI References: [1] B.N. Türkmen, E. Türkmen, A note on a generalization of injective modules , Carpathian Mathematical Publications: Vol. 12 No. 2 (2020) · Zbl 1466.16002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.