Nagoya Mathematical Journal

On the dimension of modules and algebras. II. Frobenius algebras and quasi-Frobenius rings

Samuel Eilenberg and Tadasi Nakayama

Full-text: Open access

Article information

Source
Nagoya Math. J. Volume 9 (1955), 1-16.

Dates
First available in Project Euclid: 14 June 2005

Permanent link to this document
http://projecteuclid.org/euclid.nmj/1118799677

Mathematical Reviews number (MathSciNet)
MR0073577

Zentralblatt MATH identifier
0068.26503

Subjects
Primary: 09.3X

Citation

Eilenberg, Samuel; Nakayama, Tadasi. On the dimension of modules and algebras. II. Frobenius algebras and quasi-Frobenius rings. Nagoya Mathematical Journal 9 (1955), 1--16. http://projecteuclid.org/euclid.nmj/1118799677.


Export citation

References

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

See also

  • See also: Samuel Eilenberg, Masatoshi Ikeda, Tadasi Nakayama. On the dimension of modules and algebras. I. Nagoya Mathematical Journal vol. 8, (1955), pp. 49-57.
  • See also: Maurice Auslander. On the dimension of modules and algebras. III. Global dimension. Nagoya Mathematical Journal vol. 9, (1955), pp. 67-77.
  • See also: Samuel Eilenberg, Hirosi Nagao, Tadasi Nakayama. On the dimension of modules and algebras. IV. Dimension of residue rings of hereditary rings. Nagoya Mathematical Journal vol. 10, (1956), pp. 87-95.
  • See also: Samuel Eilenberg, Tadasi Nakayama. On the dimension of modules and algebras. V. Dimension of residue rings. Nagoya Mathematical Journal vol. 11, (1957), pp. 9-12.
  • See also: Maurice Auslander. On the dimension of modules and algebras. VI. Comparison of global and algebra dimension. Nagoya Mathematical Journal vol. 11, (1957), pp. 61-65.