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On injective hulls of simple modules

✍ Scribed by Y. Hirano

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
537 KB
Volume
225
Category
Article
ISSN
0021-8693

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✦ Synopsis

We characterize a ring over which every left module of finite length has an injective hull of finite length. Using this, we show that finite normalizing extensions of such a ring also have the same property. We also consider rings having the property that the injective hull of every simple module is artinian. We show that certain noncommutative noetherian rings have this property.

πŸ“œ SIMILAR VOLUMES

On localization of injective modules
On localization of injective modules
✍ C. NaudΓ©; G. NaudΓ© πŸ“‚ Article πŸ“… 1986 πŸ› Elsevier Science 🌐 English βš– 346 KB
On the Number of Injective Indecomposabl
On the Number of Injective Indecomposable Modules
✍ Hans-Heinrich Brungs; GΓΌnter TΓΆrner πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 158 KB

For every natural number m, there exists a noncommutative valuation ring R with a completely prime ideal P so that there are exactly m nonisomorphic indecomposable injective right R-modules with P as associated prime ideal.

Injectivity of Quasi-projective Modules,
Injectivity of Quasi-projective Modules, Projectivity of Quasi-injective Modules, and Projective Cover of Injective Modules
✍ Y. Baba πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 747 KB

In [K. R. Fuller, on indecomposable injectives over artinian rings, Pacific J. Math. 29 (1969), 115-135, Theorem 3.1] K. R. Fuller gave necessary and sufficient conditions for projective left modules to be injective over a left artinian ring. In [Y. Baba and K. Oshiro, On a theorem of Fuller, prepri