✦ LIBER ✦
An Independence Result on Cotorsion Theories over Valuation Domains
✍ Scribed by S Bazzoni; L Salce
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 192 KB
- Volume
- 243
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
It is shown that, over suitable valuation domains R with field of quotients Q, the cotorsion theory K generated by K = Q/R coincides with the cotorsion theory ∂ cogenerated by the Fuchs' divisible module ∂, provided that Gödel's Axiom of Constructibility V = L is assumed. On the other hand, assuming Martin's Axiom and the negation of the Continuum Hypothesis, it is proved that the cotorsion theory K is strictly smaller than ∂ by exhibiting a strongly ℵ 1 -K -free divisible module M of projective dimension 2 such that Ext 1 R M K = 0. Applications to Whitehead modules are derived.