On Ext 1 R (A, R) for torsion-free A
Research output: Contribution to journal › Journal article › Research › peer-review
For an integral domain R with quotient field Q the group Ext R 1 (Q,R) may be regarded as a Q -vector space and hence it is isomorphic to the direct power Q (d) for some finite or infinite cardinal number d . It is shown that in the class of all Noetherian domains of Krull dimension 1 that are analytically unramified in at least one maximal ideal the above number d is either arbitrarily infinite or of the form p t −1 , p a prime. Further, a class of principal ideal domains is obtained, for which Ext R 1 (A,R)≅Q/R for a suitable torsion-free R -module A .
|Journal||Bulletin of the American Mathematical Society|
|Publication status||Published - 1972|