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We investigate some properties of -submodules. More precisely, we find a necessary and sufficient condition for every proper submodule of a module to be an -submodule. Also, we show that if is a finitely generated -module and is a prime ideal of , then has -submodule. Moreover, we define the notion of -submodule, which is a generalization of the notion of -submodule. We find some characterizations of -submodules and we examine the way the aforementioned notions are related to each...
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