**Memoirs of the American Mathematical Society**

1993;
140 pp;
Softcover

MSC: Primary 16; 20;

Print ISBN: 978-0-8218-2554-9

Product Code: MEMO/103/492

List Price: $40.00

AMS Member Price: $24.00

MAA Member Price: $36.00

**Electronic ISBN: 978-1-4704-0069-9
Product Code: MEMO/103/492.E**

List Price: $40.00

AMS Member Price: $24.00

MAA Member Price: $36.00

# Categories of Modules over Endomorphism Rings

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*Theodore G. Faticoni*

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.

#### Readership

Research mathematicians.

#### Table of Contents

# Table of Contents

## Categories of Modules over Endomorphism Rings

- Contents v6 free
- 1 Introduction and Preliminaries 114 free
- 2 Construction of the Categories 1528
- 3 Tensor and Horn Functors 3346
- 4 Category Equivalences 4760
- 5 Special Morphisms 6073
- 6 Category Equivalences for H[sub(A)] 7588
- 7 Projective Properties in μ(P[sub(A)] 97110
- 8 Injective Properties 113126
- Bibliography 129142
- Index 136149 free