On Rad-⊕-Supplemented Modules

Yahya Talebi, Azadeh Mahmoudi

Abstract


Let R be a ring and M a right R-module. M is called Rad-⊕-s-module if every submodule of M has a Rad-supplement that is a direct summand of M, and M is called completely Rad-⊕-s-module if every direct summand of M is Rad-⊕-s-module. In this paper various properties of such modules are developed. It is shown that any finite direct sum of Rad-⊕-s-modules is Rad-⊕-s-module. We also show that if M is Rad-⊕-s-module with (D3), then M is completely Rad-⊕-s-module.

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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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|ISSN 1686-0209|