A module is said to be extending if every submodule is essential in a direct summand of the module. In this paper, we define and investigate in details extending notion and its two generalizations in terms of a left exact preradical in the category of right modules. Our results are based on structural and decomposition properties of these new classes of modules. Examples are included on using special left exact preradicals.
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Mutlu et al. (2024) studied this question.
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