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Categories of Modules over Endomorphism Rings
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The goal of this work is to develop a functional transfer of properties between a module A and the category *M *E of right modules over its endomorphism ring *E that is more sensitive than the traditional starting point Hom (A, .). The main result is a factorization q *[A t*[ of the left adjoint T *A of Hom(, .), where t*[ is a category equivalence and q*[ is a forgetful functor. Applications include a characterization of the finitely generated submodules of the right *E-modules Hom (*A), a connection between quasi-projective modules and flat modules, an extension of some recent work on endomo...
The goal of this work is to develop a functional transfer of properties between a module A and the category *M *E of right modules over its endomorphism ring *E that is more sensitive than the traditional starting point Hom (A, .). The main result is a factorization q *[A t*[ of the left adjoint T *A of Hom(, .), where t*[ is a category equivalence and q*[ is a forgetful functor. Applications include a characterization of the finitely generated submodules of the right *E-modules Hom (*A), a connection between quasi-projective modules and flat modules, an extension of some recent work on endomorphism rings of *S-quasi-projective modules, an extension of Fuller's Theorem, characterizations of several self-generating properties and injective properties, and a connection between *S-self-generators and quasi-projective modules.