On non-\(M\)-cosingular completely \(\oplus\)-supplemented modules. (English) Zbl 1137.16005
Summary: It is shown that any non-\(M\)-cosingular \(\oplus\)-supplemented module \(M\) is \((D_3)\) if and only if \(M\) has the summand intersection property. Let \(N\in\sigma[M]\) be any module such that \(\overline Z_M(N)\) has a coclosure in \(N\). Then we prove that \(N\) is (completely) \(\oplus\)-supplemented if and only if \(N=\overline Z_M^2(N)\oplus K\) for some submodule \(K\) of \(N\) such that \(\overline Z_M^2(N)\) and \(K\) both are (completely) \(\oplus\)-supplemented.
MSC:
| 16D70 | Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) |
| 16D40 | Free, projective, and flat modules and ideals in associative algebras |
Keywords:
pseudo projective modules; non-cosingular modules; completely \(\oplus\)-supplemented modules; summand intersection propertyReferences:
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