Categories of Modules over Endomorphism Rings

Categories of Modules over Endomorphism Rings

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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, $\mathrm{Hom}(A, \cdot )$. The main result is a factorization $\mathrm{q}_{A}\mathrm{t}_{A}$ of the left adjoint $\mathrm{T}_{A}$ of $\mathrm{Hom}(A, \cdot )$, where $\mathrm{t}_{A}$ is a category equivalence and $\mathrm{ q}_{A}$ is a forgetful functor. Applications include a characterization of the finitely generated submodules of the right $E$-modules $\mathrm{Hom}(A, G)$, 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.To be published in the Memoirs, a paper must be correct, new, nontrivial, and significant. ... As of March 1, 1993, the backlog for this journal was approximately 7 volumes. ... The paper must contain a descriptive title and an abstract that summarizes the article in language suitable for workers in the general field ( algebra, anbsp;...

Title:Categories of Modules over Endomorphism Rings
Author:Theodore G. Faticoni
Publisher:American Mathematical Soc. - 1993


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