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ON ω-LOCAL MODULES AND Rad-SUPPLEMENTED MODULES

  • Buyukasik, Engin ;
  • Tribak, Rachid
  • Received : 2013.10.11
  • Published : 2014.09.01

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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