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
.
Original language | English |
---|---|
Journal | Bulletin of the American Mathematical Society |
Volume | 78 |
Issue number | 5 |
Pages (from-to) | 831-834 |
ISSN | 0273-0979 |
Publication status | Published - 1972 |
ID: 152957324