<abstract xmlns="http://www.w3.org/1999/xhtml"> Let M be a right R-module. We call M Rad-D12, if for every sub- module N of M, there exist a direct summand K of M and an epimor- phism α : K → M/N such that Kererα ⊆ Rad(K). We show that a direct summand of a Rad-D12 module need not be a Rad-D12 module. We investigate completely Rad-D12 modules (modules for which every direct summand is a Rad-D12 module). We also show that a direct sum of Rad-D12 modules need not be a Rad-D12 module. Then we deal with some cases of direct sums of Rad-D12 modules.</abstract>

Let M be a right R-module. We call M Rad-D12, if for every sub- module N of M, there exist a direct summand K of M and an epimor- phism α : K → M/N such that Kererα ⊆ Rad(K). We show that a direct summand of a Rad-D12 module need not be a Rad-D12 module. We investigate completely Rad-D12 modules (modules for which every direct summand is a Rad-D12 module). We also show that a direct sum of Rad-D12 modules need not be a Rad-D12 module. Then we deal with some cases of direct sums of Rad-D12 modules.

On Rad-D12 Modules

Department of Mathematics, University of Mazandaran, Babolsar, Iran

Department of Mathematics, University of Hacettepe, 06800 Beytepe, Ankara, Turkey

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

{"article-title":"On Rad-D12 Modules"}

Let M be a right R-module. We call M Rad-D12, if for every sub- module N of M, there exist a direct summand K of M and an epimor- phism α : K → M/N such that...

On Rad-D12 Modules

Publié en ligne: 30 juil. 2013

Pages: 201 - 208

DOI: https://doi.org/10.2478/auom-2013-0012

This content is open access.