On Ext 1 R (A, R)  for torsion-free A

Chr Ulrik Jensen

On Ext 1 R (A, R) for torsion-free A

Institut for Matematiske Fag

6 Citationer (Scopus)

Abstract

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 .

Originalsprog	Engelsk
Tidsskrift	Bulletin of the American Mathematical Society
Vol/bind	78
Udgave nummer	5
Sider (fra-til)	831-834
ISSN	0273-0979
Status	Udgivet - 1972

Citationsformater

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T1 - On Ext 1 R (A, R) for torsion-free A

AU - Jensen, Chr Ulrik

PY - 1972

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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

SN - 0273-0979

VL - 78

SP - 831

EP - 834

JO - Bulletin of the American Mathematical Society

JF - Bulletin of the American Mathematical Society

IS - 5

ER -