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Yahya Talebi, Behnam Talaee, Mohammad Javad Nematollahi


A module M is said to satisfy the Rad - Di condition (i = 1, 2, 3) if, M satisfies the Di condition for every submodule which is contained in Rad(M). We show that a Rad -quasi-projective module satisfies the Rad-D2 and Rad-D3 conditions and every direct summand of a Rad-D1 module is also Rad-D1. Also we show that for a module M, every module is weakly Rad -M-projective if and only if Rad(M) is a direct summand of M.


Supplemented modules, Rad-projective modules, Rad-Di modules.

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