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http://dx.doi.org/10.4134/JKMS.2014.51.5.971

ON ω-LOCAL MODULES AND Rad-SUPPLEMENTED MODULES  

Buyukasik, Engin (Izmir Institute of Technology Department of Mathematics)
Tribak, Rachid (Centre Regional des Metiers de l'Education et de la Formation (CRMEF)-Tanger)
Publication Information
Journal of the Korean Mathematical Society / v.51, no.5, 2014 , pp. 971-985 More about this Journal
Abstract
All modules considered in this note are over associative commutative rings with an identity element. We show that a ${\omega}$-local module M is Rad-supplemented if and only if M/P(M) is a local module, where P(M) is the sum of all radical submodules of M. We prove that ${\omega}$-local nonsmall submodules of a cyclic Rad-supplemented module are again Rad-supplemented. It is shown that commutative Noetherian rings over which every w-local Rad-supplemented module is supplemented are Artinian. We also prove that if a finitely generated Rad-supplemented module is cyclic or multiplication, then it is amply Rad-supplemented. We conclude the paper with a characterization of finitely generated amply Rad-supplemented left modules over any ring (not necessarily commutative).
Keywords
${\omega}$-local modules; Rad-supplemented modules; amply Rad-supplemented modules;
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