ON ω-LOCAL MODULES AND Rad-SUPPLEMENTED MODULES

Title & Authors
ON ω-LOCAL MODULES AND Rad-SUPPLEMENTED MODULES

Abstract
All modules considered in this note are over associative commutative rings with an identity element. We show that a $\small{{\omega}}$-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 $\small{{\omega}}$-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
$\small{{\omega}}$-local modules;Rad-supplemented modules;amply Rad-supplemented modules;
Language
English
Cited by
1.
RAD-SUPPLEMENTING MODULES, Journal of the Korean Mathematical Society, 2016, 53, 2, 403
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