Linearly compact modules over Noetherian rings
β Scribed by Syed M Fakhruddin
- Publisher
- Elsevier Science
- Year
- 1973
- Tongue
- English
- Weight
- 357 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
For several classes of commutative rings R it is known that every finitely generated projective R-modules is isomorphic to a direct sum of a free w x R-module and an invertible ideal of R. For instance, Steinitz 27 essenw x tially proved this for Dedekind domains. Serre 25 proved the same result for
We show that the following two conditions, for each integer r G 1, are equivalent for a finitely generated module M over a complete Noetherian local ring Ε½ . R, α : embeddable in E r , where E denotes the injective hull of the residue field Rrα. Ε½ . r Ε½ . b Either M ; E , or else dim Hom Rrα, M s k