On Ext 1 R (A, R) for torsion-free A
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On Ext 1 R (A, R) for torsion-free A . / Jensen, Chr Ulrik.
In: Bulletin of the American Mathematical Society, Vol. 78, No. 5, 1972, p. 831-834.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - On Ext 1 R (A, R) for torsion-free A
AU - Jensen, Chr Ulrik
PY - 1972
Y1 - 1972
N2 - 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 .
AB - 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 .
M3 - Journal article
VL - 78
SP - 831
EP - 834
JO - Bulletin of the American Mathematical Society
JF - Bulletin of the American Mathematical Society
SN - 0273-0979
IS - 5
ER -
ID: 152957324