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Categories of Modules over Endomorphism Rings

Available Formats:
Electronic ISBN: 978-1-4704-0069-9
Product Code: MEMO/103/492.E
List Price: $40.00 MAA Member Price:$36.00
AMS Member Price: $24.00 Click above image for expanded view Categories of Modules over Endomorphism Rings Available Formats:  Electronic ISBN: 978-1-4704-0069-9 Product Code: MEMO/103/492.E  List Price:$40.00 MAA Member Price: $36.00 AMS Member Price:$24.00
• Book Details

Memoirs of the American Mathematical Society
Volume: 1031993; 140 pp
MSC: 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 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.

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
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Volume: 1031993; 140 pp
MSC: 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 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.

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
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
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