Categories of Modules over Endomorphism
β Theodore G. Faticoni
π Library
π
1993
π Amer Mathematical Society
π English
β¦ LIBER β¦
π
Categories of Modules over Endomorphism Rings
β Scribed by Theodore G. Faticoni
- Publisher
- Amer Mathematical Society
- Year
- 1993
- Tongue
- English
- Leaves
- 159
- Series
- Memoirs of the American Mathematical Society
- Category
- Library
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β¦ Synopsis
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, $\textnormal{Hom}(A, \cdot )$. The main result is a factorization $\textnormal{q}{A}\textnormal{t}{A}$ of the left adjoint $\textnormal{T}{A}$ of $\textnormal{Hom}(A, \cdot )$, where $\textnormal{t}{A}$ is a category equivalence and $\textnormal{ q}{A}$ is a forgetful functor. Applications include a characterization of the finitely generated submodules of the right $E$-modules $\textnormal{Hom}(A,G)$, 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.
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