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On cofinitely Rad-supplemented modules. (English) Zbl 1189.16003

Summary: Let \(R\) be a ring and \(M\) be a left \(R\)-module. In this work some properties of (amply) cofinitely Rad-supplemented modules are developed. It is shown that if \(M\) contains a nonzero semi-hollow submodule then \(M\) is cofinitely Rad-supplemented if and only if \(M/N\) is cofinitely Rad-supplemented. Moreover a module \(M\) with small radical is cofinitely Rad-supplemented such that Rad-supplements are supplements in \(M\), then \(M\) is cofinitely supplemented. In addition, a ring \(R\) is left Rad-supplemented if and only if every left \(R\)-module is amply cofinitely Rad-supplemented. Also, we give a characterization of generalized semiperfect modules.

MSC:

16D70 Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)
16L30 Noncommutative local and semilocal rings, perfect rings
16D40 Free, projective, and flat modules and ideals in associative algebras
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