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The Homological Dimension of a Quotient Field

Published online by Cambridge University Press:  22 January 2016

Irving Kaplansky
Irving Kaplansky*
Affiliation:
University of Chicago
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Let R be an integral domain, Q its quotient field. For any R-module A we write d(A) for its homological dimension (minimal length of a projective resolution), or dR(A) if it is necessary to call attention to R.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 1 , February 1966 , pp. 139 - 142
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Kaplansky, I., Projective modules, Annals of Math. 68 (1958), 372–7.CrossRefGoogle Scholar
[2] Kaplansky, I., Homological dimension of rings and modules, Univ. of Chicago mimeographed notes, 1959.Google Scholar
[3] Matlis, E., Divisible modules, Proc. Amer Math. Soc. 11 (1960), 385–391.CrossRefGoogle Scholar
[4] Matlis, E., Cotorsion modules, Memoirs Amer. Math. Soc. no. 49, 1964.CrossRefGoogle Scholar