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On the Dimension of Modules and Algebras, X: A Right Hereditary Ring which is not left Hereditary

Published online by Cambridge University Press:  22 January 2016

Irving Kaplansky
Irving Kaplansky*
Affiliation:
University of Chicago
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A ring R is said to be right (left) hereditary if every right (left) ideal in R is projective, that is, a direct summand of a free R-module. Cartan and Eilenberg [3, p. 15] ask whether there exists a right hereditary ring which is not left hereditary. The answer: yes.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 13 , June 1958 , pp. 85 - 88
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1958

References

[1] Auslander, N., On the dimension of modules and algebras. III. Global dimension, Nagoya Math. J., 9 (1955), 67–77.CrossRefGoogle Scholar
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[3] Cartan, H. and Eilenberg, S., Homological Algebra, Princeon, 1956.Google Scholar
[4] Jacobson, N., Structure of Rings, Amer. Math. Soc. Coll. Pub., vol. 37, 1956.Google Scholar
[5] Zelinsky, D., Raising idempotents, Duke Math. J., 21 (1954), 315–322.Google Scholar