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Note on Relative Homological Dimension

Published online by Cambridge University Press:  22 January 2016

G. Hochschild
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Let R be a ring with identity element 1, and let S be a subring of R containing 1. We consider R-modules on which 1 acts as the identity map, and we shall simultaneously regard such R-modules as S-modules in the natural way. In [4], we have defined the relative analogues of the functors of Cartan-Eilenberg [1], and we have briefly treated the corresponding relative analogues of module dimension and global ring dimension.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 13 , June 1958 , pp. 89 - 94
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1958

References

[1] Cartan, H. and Eilenberg, S., Homological Algebra, Princeton, 1956.Google Scholar
[2] Eilenberg, S., Rosenberg, A. and Zelinsky, D., On the dimension of modules and algebras (VIII), Nagoya Math. J., Vol. 12 (1957), 71–93.Google Scholar
[3] Harada, M., Note on the dimension of modules and algebras, J. Inst. Polytech. Osaka City Univ., Ser. A. 7 (1956), 87–96.Google Scholar
[4] Hochschild, G., Relative Homological Algebra, Trans. Am. Math. Soc., Vol. 82 (1956), 246–269.Google Scholar