Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-23T23:38:55.564Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Dimension of Modules and Algebras, II: (Frobenius Algebras and Quasi-Frobenius Rings)

Published online by Cambridge University Press:  22 January 2016

Samuel Eilenberg  and
Tadasi Nakayama
Samuel Eilenberg
Affiliation:
Columbia University
Tadasi Nakayama
Affiliation:
Nagoya University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we study Frobenius algebras and quasi-Frobenius rings with particular emphasis on their cohomological dimensions. For definitions of these cohomological dimensions we refer the reader to Cartan-Eilenberg [3] or Eilenberg [4].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 9 , October 1955 , pp. 1 - 16
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1955

References

[1] Baer, R., Abelian groups that are direct summands of every containing abelian group, Bull. Amer. Math. Soc. 46 (1940), 800–806.CrossRefGoogle Scholar
[2] Nesbitt, R. Brauer-C., On the regular representations of algebras, Proc. Nat. Acad. Sci. U.S.A. 23 (1937), 236–240.Google Scholar
[3] Eilenberg, H. Cartan-S., Homological Algebra, Princeton Univ. Press, 1955.Google Scholar
[4] Eilenberg, S., Algebras of cohomological finite dimension, Comment. Math. Helv. 28 (1954), 310–319.Google Scholar
[5] Eilenberg-M., S. Nakayama, Ikeda-T., On the dimension of modules and algebras, I, Nagoya Math. J. 8 (1955).CrossRefGoogle Scholar
[6] Hochschild, G., Cohomology and representations of associative algebras, Duke Math. J. 14 (1947), 921–948.Google Scholar
[7] Ikeda, M., A characterization of quasi-Frobenius rings, Csaka Math. J. 4 (1952), 203–210.Google Scholar
[8] Ikeda-H., M. Nakayama, Nagao-T., Algebras with vanishing n-cohomology groups, Nagoya Math. J. 7 (1954).CrossRefGoogle Scholar
[9] Nakayama, M. Ikeda-T., On some characteristic properties of quasi-Frobenius and regular rings, Bull. Amer. Math. Soc. 5 (1954), 15–19.Google Scholar
[10] Nakayama, H. Nagao-T., On the structure of (M 0)- and (Mu )-modules, Math. Zeits. 59 (1953), 164–170.Google Scholar
[11] Nakayama, T., On Frobeniusean algebras, I, Ann. Math. 40 (1939), 611–633.Google Scholar
[12] Nakayama, T., On Frobeniusean algebras, II, Ann. Math. 42 (1941), 1–21.Google Scholar
[13] Nesbitt, C., On the regular representation of algebras, Ann. of Math. 39 (1938), 634–658.Google Scholar