1-torsion of finite modules over semiperfect rings (Q619017)

For any \(\Lambda\)-module \(M\), the \(1\)-torsion submodule of \(M\) is defined as the kernel of the canonical map \(M\to M^{**}\), where \(M^*=\Hom_{\Lambda}(M,\Lambda)\). The paper initiates the study of \(1\)-torsion of finite modules over two-sided noetherian semiperfect rings. Among other results, the author gives a criterion for determining when the \(1\)-torsion submodule contains minimal generators of the module, and provides an explicit construction for a projective cover of the submodule generated by the torsion elements in the top of the module.