Memoirs of the American Mathematical Society 1993; 140 pp; softcover Volume: 103 ISBN10: 0821825542 ISBN13: 9780821825549 List Price: US$38 Individual Members: US$22.80 Institutional Members: US$30.40 Order Code: MEMO/103/492
 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, \(\mathrm{Hom}(A, \cdot )\). 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 quasiprojective modules and flat modules, an extension of some recent work on endomorphism rings of \(\Sigma\)quasiprojective modules, an extension of Fuller's Theorem, characterizations of several selfgenerating properties and injective properties, and a connection between \(\Sigma\)selfgenerators and quasiprojective modules. Readership Research mathematicians. Table of Contents  Construction of the categories
 Tensor and \(\operatorname{Hom}\) functors
 Category equivalences
 Special morphisms
 Category Equivalences for \(H_A\)
 Projective properties in \({\mathcal M}({\mathcal P}_A)\)
 Injective properties
