Electronic ISBN:  9781470400699 
Product Code:  MEMO/103/492.E 
List Price:  $40.00 
MAA Member Price:  $36.00 
AMS Member Price:  $24.00 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 103; 1993; 140 ppMSC: Primary 16; 20;
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.
ReadershipResearch mathematicians.

Table of Contents

Chapters

1. Introduction and preliminaries

2. Construction of the categories

3. Tensor and horn functors

4. Category equivalences

5. Special morphisms

6. Category equivalences for $\mathrm {H}_A$

7. Projective properties in $\mathcal {M}(\mathcal {P}_A)$

8. Injective properties


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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 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.
Research mathematicians.

Chapters

1. Introduction and preliminaries

2. Construction of the categories

3. Tensor and horn functors

4. Category equivalences

5. Special morphisms

6. Category equivalences for $\mathrm {H}_A$

7. Projective properties in $\mathcal {M}(\mathcal {P}_A)$

8. Injective properties