A note on modules with \((D_{11}^+)\). (English) Zbl 1101.16005
Summary: Let \(R\) be a ring and \(M\) a left \(R\)-module. Then, \(M\) is called a \((D_{11})\)-module if every submodule of \(M\) has a supplement that is a direct summand of \(M\), and \(M\) is called a \((D^{+}_{11})\)-module if every direct summand of \(M\) is a \((D_{11})\)-module. In this paper, the author characterizes the \((D^{+}_{11})\)-module \(N\in\delta[M]\) in terms of \(\overline Z^2_M(N)\).
MSC:
16D50 | Injective modules, self-injective associative rings |
16D70 | Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) |