Modules with every subgenerated module lifting
In a recent paper of \textit{S. T. Rizvi} and the reviewer [On some classes of Artinian rings (to appear)], a module \(M\) is defined to be CS-semisimple if every module in \(\sigma[M]\) is CS. By a result of N. V. Dung and P. F. Smith (1992), a module \(M\) is CS-semisimple if and only if \(M\) is a direct sum of simple modules and uniform \(M\)-injective modules of length 2. In the paper under review, the authors prove that a module \(M\) is CS-semisimple if and only if every module in \(\sigma[M]\) is lifting.
scientific article; zbMATH DE number 880187