• East Asian mathematical journal
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• v.19 no.2
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• pp.251-259
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• 2003

The concepts of t-rational extensions and t-essential extensions of modules, where t a preradical for R-Mod, are introduced. The structures of such extensions are determined. Relations between maximal t-rational extensions and other concepts of modules are studied.

• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1069-1083
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• 2016

In this paper, the structure of e-local modules and classes of modules via essentially small are investigated. We show that the following conditions are equivalent for a module M: (1) M is e-local; (2) $Rad_e(M)$ is a maximal submodule of M and every proper essential submodule of M is contained in a maximal submodule; (3) M has a unique essential maximal submodule and every proper essential submodule of M is contained in a maximal submodule.