Completely faithful modules and quasi-Frobenius algebras

Shizuo ENDO

doi:10.2969/jmsj/01940437

Shizuo ENDO

Author information

JOURNAL FREE ACCESS

1967 Volume 19 Issue 4 Pages 437-456

DOI https://doi.org/10.2969/jmsj/01940437

Details

Published: 1967 Received: October 01, 1966 Available on J-STAGE: September 26, 2006 Accepted: - Advance online publication: - Revised: -
Correction information
Date of correction: September 26, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) M. Auslander and O. Goldman, Maximal orders, Trans. Amer. Math. Soc., 97 (1960), 1-24.
2) M. Auslander and O. Goldman, The Brauer group of a commutative ring, Trans. Amer. Math. Soc., 97 (1960), 367-409.
3) G. Azumaya and T. Nakayama, Algebra II, Iwanami, Tokyo, 1954 (in Japanese).
4) G. Azumaya, Completely faithful modules and self-injective rings, Nagoya Math. J., 27 (1966), 697-708.
5) H. Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc., 95 (1960), 466-488.
6) H. Bass, The Morita theorems, Lecture note at Univ. of Oregon, 1962 (mineo-graphed note).
7) H. Bass, K-theory and stable algebras, Publ. de L'Institut des Haute Etudes Sci., 1964, N 22, 489-544.
8) H. Cartan and S. Eilenberg, Homological algebra, Princeton Univ. Press, 1956.
9) C. Curtis and I. Reiner, Representation theory of finite groups and algebras, Interscience, 1962.
10) S. Eilenberg and T. Nakayama, On the dimensions of modules and algebras, II, Nagoya Math. J., 9 (1955), 1-16.
11) P. Gabriel, Des catégories abéliennes, Bull. Soc. Math. France, 90 (1962), 323-448.
12) A. Grothendieck, Sur quelques points d'algebre homologique, Tohoku Math. J., 9 (1957), 119-220.
13) M. Harada, Hereditary orders, Trans. Amer. Math. Soc., 107 (1963), 273-290.
14) A. Hattori, Semi-simple algebras over a commutative ring, J. Math. Soc. Japan, 15 (1963), 404-419.
15) A. Hattori, Semi-simple algebras over a commutative ring, Proc. Symp. Algebra, Math. Soc. Japan, 6 (1965), 37-40, (in Japanese).
16) A. Hattori, Simple algebras over a commutative ring, Nagoya Math. J., 27 (1966), 611-616.
17) E. Matlis, Injective modules over Noetherian rings, Pacific J. Math., 8 (1958), 511-528.
18) K. Morita, Duality for modules and its application to the theory of rings with minimum condition, Sci. Rep. Tokyo Kyoiku Daigaku, Sect. A, 6 (1958), 83-142.
19) B. Müller. Quasi-Frobenius Erweiterungen, Math. Zeit., 85 (1964), 345-368.
20) B. Müller, Quasi-Frobenius Erweiterungen II, Math. Zeit., 88 (1965), 380-409.
21) M. Nagata, Local rings, Interscience, 1962.
22) T. Nakayama and T. Tsuzuku, On Frobenius extensions 1, Nagoya Math. J., 17 (1960), 89-110.

Right : [1] M. Auslander and O. Goldman, Maximal orders, Trans. Amer. Math. Soc., 97 (1960), 1-24.
[2] M. Auslander and O. Goldman, The Brauer group of a commutative ring, Trans. Amer. Math. Soc., 97 (1960), 367-409.
[3] G. Azumaya and T. Nakayama, Algebra II, Iwanami, Tokyo, 1954 (in Japanese).
[4] G. Azumaya, Completely faithful modules and self-injective rings, Nagoya Math. J., 27 (1966), 697-708.
[5] H. Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc., 95 (1960), 466-488.
[6] H. Bass, The Morita theorems, Lecture note at Univ. of Oregon, 1962 (mineo-graphed note).
[7] H. Bass, K-theory and stable algebras, Publ. de L'Institut des Haute Etudes Sci., 1964, N 22, 489-544.
[8] H. Cartan and S. Eilenberg, Homological algebra, Princeton Univ. Press, 1956.
[9] C. Curtis and I. Reiner, Representation theory of finite groups and algebras, Interscience, 1962.
[10] S. Eilenberg and T. Nakayama, On the dimensions of modules and algebras, II, Nagoya Math. J., 9 (1955), 1-16.
[11] P. Gabriel, Des catégories abéliennes, Bull. Soc. Math. France, 90 (1962), 323-448.
[12] A. Grothendieck, Sur quelques points d'algebre homologique, Tôhoku Math. J., 9 (1957), 119-220.
[13] M. Harada, Hereditary orders, Trans. Amer. Math. Soc., 107 (1963), 273-290.
[14] A. Hattori, Semi-simple algebras over a commutative ring, J. Math. Soc. Japan, 15 (1963), 404-419.
[15] A. Hattori, Semi-simple algebras over a commutative ring, Proc. Symp. Algebra, Math. Soc. Japan, 6 (1965), 37-40, (in Japanese).
[16] A. Hattori, Simple algebras over a commutative ring, Nagoya Math. J., 27 (1966), 611-616.
[17] E. Matlis, Injective modules over Noetherian rings, Pacific J. Math., 8 (1958), 511-528.
[18] K. Morita, Duality for modules and its application to the theory of rings with minimum condition, Sci. Rep. Tokyo Kyoiku Daigaku, Sect. A, 6 (1958), 83-142.
[19] B. Müller. Quasi-Frobenius Erweiterungen, Math. Zeit., 85 (1964), 345-368.
[20] B. Müller, Quasi-Frobenius Erweiterungen II, Math. Zeit., 88 (1965), 380-409.
[21] M. Nagata, Local rings, Interscience, 1962.
[22] T. Nakayama and T. Tsuzuku, On Frobenius extensions I, Nagoya Math. J., 17 (1960), 89-110.

Date of correction: September 26, 2006 Reason for correction: - Correction: PDF FILE Details: -

Corresponding author

Correction information

Register with J-STAGE for free!