On Rad-D-12 Modules

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Talebi Y., HAMZEKOLAEE A. R. M., Tutuncu D. K.

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, vol.21, no.1, pp.201-208, 2013 (SCI-Expanded) identifier identifier


Let M be a right R-module. We call M Rad-D-12, if for every submodule N of M, there exist a direct summand K of M and an epimorphism alpha : K -> M/N such that Ker alpha subset of Rad(K). We show that a direct summand of a Rad-D-12 module need not be a Rad-D-12 module. We investigate completely Rad-D-12 modules (modules for which every direct summand is a Rad-D-12 module). We also show that a direct sum of Rad-D-12 modules need not be a Rad-D-12 module. Then we deal with some cases of direct sums of Rad-D-12 modules.