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Nagoya Mathematical Journal

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

Samuel Eilenberg and Tadasi Nakayama
Source: Nagoya Math. J. Volume 9 (1955), 1-16.
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Primary Subjects: 09.3X
Full-text: Open access
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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.nmj/1118799677
Mathematical Reviews number (MathSciNet): MR0073577
Zentralblatt MATH identifier: 0068.26503

References

[1] R. Baer, Abelian groups that are direct summands of every containing abelian group, Bull. Amer. Math. Soc. 46(1940), 800-806.
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
Zentralblatt MATH: 0029.34201
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.
Mathematical Reviews (MathSciNet): MR14:719d
Zentralblatt MATH: 0048.02501
[8] M. Ikeda-H. Nagao-T. Nakayama, Algebras with vanishing w-cohomology groups, Nagoya Math. J. 7(1954).
Mathematical Reviews (MathSciNet): MR16:214f
Zentralblatt MATH: 0058.02703
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
Zentralblatt MATH: 0051.26305
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
Zentralblatt MATH: 0021.29402
Digital Object Identifier: doi:10.2307/1968946
[12] T. Nakayama, On Frobeniusean algebras, II, Ann. Math. 42 (1941), 1-21.
Mathematical Reviews (MathSciNet): MR2:344b
Zentralblatt MATH: 67.0092.04
Digital Object Identifier: doi:10.2307/1968984
[13] C. Nesbitt, On the regular representation of algebras, Ann. of Math. 39 (1938), 634-658. Columbia University Nagoya University
Mathematical Reviews (MathSciNet): MR1503429
Zentralblatt MATH: 0019.10201
Digital Object Identifier: doi:10.2307/1968639

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