Classes of Modules Related to Serre Subcategories
نویسندگان
چکیده
Let R be an associative ring with non-zero identity. For a Serre subcategory C of the category R-mod of left R-modules, we consider the class AC of all modules that do not belong to C, but all of their proper submodules belong to C. Alongside of basic properties of such associated classes of modules, we will prove that every uniform module of AC has a local endomorphism ring. Moreover, if R is a commutative ring, then every torsionfree faithful R-module of AC is isomorphic to the injective hull of R and its endomorphism ring is a division ring.
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