Nagoya Mathematical Journal

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

Samuel Eilenberg and Tadasi Nakayama

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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
https://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 Math. J. 9 (1955), 1--16. https://projecteuclid.org/euclid.nmj/1118799677


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References

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    Mathematical Reviews (MathSciNet): MR2:126i
    Zentralblatt MATH: 0024.14902
    Digital Object Identifier: doi:10.1090/S0002-9904-1940-07306-9
    Project Euclid: euclid.bams/1183503234
  • [2] R. Brauer-C. Nesbitt, On the regular representations of algebras, Proc. Nat. Acad. Sci. U.S.A. 23(1937), 236-240.
    Mathematical Reviews (MathSciNet): MR1503429
    Zentralblatt MATH: 0019.10201
    Digital Object Identifier: doi:10.2307/1968639
  • [3] H. Cartan-S. Eilenberg, Homological Algebra, Princeton Univ. Press, 1955.
    Mathematical Reviews (MathSciNet): MR1731415
  • [4] S. Eilenberg, Algebras of cohomological finite dimension, Comment. Math. Helv. 28 (1954), 310-319.
    Mathematical Reviews (MathSciNet): MR16:442c
    Zentralblatt MATH: 0058.02801
    Digital Object Identifier: doi:10.1007/BF02566937
  • [5] S. Eilenberg-M. Ikeda-T. Nakayama, On the dimension of modules and algebras, I, Nagoya Math. J. 8(1955).
    Mathematical Reviews (MathSciNet): MR16:993a
    Zentralblatt MATH: 0066.28801
    Project Euclid: euclid.nmj/1118799619
  • [6] G. Hochschild, Cohomology and representations of associative algebras, Duke Math. J. 14(1947), 921-948.
    Mathematical Reviews (MathSciNet): MR9:267b
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    Digital Object Identifier: doi:10.1215/S0012-7094-47-01473-7
    Project Euclid: euclid.dmj/1077474484
  • [7] M. Ikeda, A characterization of quasi-Frobenius rings, Csaka Math. J. 4 (1952), 203-210.
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  • [8] M. Ikeda-H. Nagao-T. Nakayama, Algebras with vanishing w-cohomology groups, Nagoya Math. J. 7(1954).
    Mathematical Reviews (MathSciNet): MR16:214f
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    Project Euclid: euclid.nmj/1118799563
  • [9] M. Ikeda-T. Nakayama, On some characteristic properties of quasi-Frobenius and regular rings, Bull. Amer. Math. Soc. 5(1954), 15-19.
    Mathematical Reviews (MathSciNet): MR15:677b
    Zentralblatt MATH: 0055.02602
    Digital Object Identifier: doi:10.1090/S0002-9939-1954-0060489-9
  • [10] H. Nagao-T. Nakayama, On the structure of Mo)- and (Mn)-modules, Math. Zeits. 59 (1953), 164-170.
    Mathematical Reviews (MathSciNet): MR15:195a
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    Digital Object Identifier: doi:10.1007/BF01180248
  • [11] T. Nakayama, On Frobeniusean algebras, I, Ann. Math. 40 (1939), 611-633.
    Mathematical Reviews (MathSciNet): MR1:3a
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  • [12] T. Nakayama, On Frobeniusean algebras, II, Ann. Math. 42 (1941), 1-21.
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  • [13] C. Nesbitt, On the regular representation of algebras, Ann. of Math. 39 (1938), 634-658. Columbia University Nagoya University
    Mathematical Reviews (MathSciNet): MR1503429
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    Digital Object Identifier: doi:10.2307/1968639

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.
    Project Euclid: euclid.nmj/1118799619
  • See also: Maurice Auslander. On the dimension of modules and algebras. III. Global dimension. Nagoya Mathematical Journal vol. 9, (1955), pp. 67-77.
    Project Euclid: euclid.nmj/1118799684
  • 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.
    Project Euclid: euclid.nmj/1118799771
  • 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.
    Project Euclid: euclid.nmj/1118799855
  • 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.
    Project Euclid: euclid.nmj/1118799859

Nagoya Mathematical Journal

Nagoya Mathematical Journal
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