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
On localization of injective modules
✍ Scribed by C. Naudé; G. Naudé
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 346 KB
- Volume
- 103
- Category
- Article
- ISSN
- 0021-8693
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📜 SIMILAR VOLUMES
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.
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
However, while a right ⌺-pure-injective ring is semiprimary with maximum condition on annihilator right ideals, a right pure-injective ring is only Von Neumann regular modulo the radical with the idempotent-lifting property 200