Uniform modules over serial rings
✍ Scribed by Bruno J Müller; Surjeet Singh
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 852 KB
- Volume
- 144
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
📜 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 Ž . R, ᒊ : embeddable in E r , where E denotes the injective hull of the residue field Rrᒊ. Ž . r Ž . b Either M ; E , or else dim Hom Rrᒊ, M s k