Categories of modules over endomorphism rings Theodore G. Faticoni. Memoirs of the American Mathematical Society 492.. This item is unavailable.Categories of modules over endomorphism rings Theodore G. Faticoni. Memoirs of the American Mathematical Society 492.

The goal of this work is to develop a functorial transfer of properties between a module $A$ and the category ${\mathcal M}_{E}$ of right modules over its endomorphism ring, $E$, that is more sensitive than the traditional starting point, $\textnormal{Hom}(A, \cdot )$. The main result is a factorization $\textnormal{q}_{A}\textnormal{t}_{A}$ of the left adjoint $\textnormal{T}_{A}$ of $\textnormal{Hom}(A, \cdot )$, where $\textnormal{t}_{A}$ is a category equivalence and $\textnormal{ q}_{A}$ is a forgetful functor. Applications include a characterization of the finitely generated submodules of the right $E$-modules $\textnormal{Hom}(A,G)$, a connection between quasi-projective modules and flat modules, an extension of some recent work on endomorphism rings of $\Sigma$-quasi-projective modules, an extension of Fuller's Theorem, characterizations of several self-generating properties and injective properties, and a connection between $\Sigma$-self-generators and quasi-projective modules.