@article{PDML_1974__11_2_19_0,
author = {Harada, Manabu},
title = {Applications of Factor Categories to Completely Indecomposable Modules},
journal = {Publications du D\'epartement de math\'ematiques (Lyon)},
volume = {11},
year = {1974},
pages = {19-104},
mrnumber = {364356},
zbl = {0335.13006},
language = {en},
url = {http://dml.mathdoc.fr/item/PDML_1974__11_2_19_0}
}
Harada, Manabu. Applications of Factor Categories to Completely Indecomposable Modules. Publications du Département de mathématiques (Lyon), Tome 11 (1974) pp. 19-104. http://gdmltest.u-ga.fr/item/PDML_1974__11_2_19_0/
[1] , Correction and supplementaires to my paper concering Krull-Remak-Schmidt'theorem, Nagoya Math. J. 1 (1950). | MR 37832 | Zbl 0040.01201
[2] , Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960). | MR 157984 | Zbl 0094.02201
[3] , Direct products of modules, Trans. Amer. Math. Soc. 97 (1960). | MR 120260 | Zbl 0100.26602
[4] and , Refinements for infinite direct decomposition of algebraic system, Pacific J. Math. 14 (1964). | MR 169806 | Zbl 0134.25504
[5] , Catégories et structures, Dunod, Paris, 1965. | MR 213410 | Zbl 0136.25801
[6] , Zu dem Satz von Krull-Remak-Schmidt-Azumaya, Math. Z. 115 (1970). | MR 269687 | Zbl 0188.09001
[7] , Interdirekte Summen von Moduln, J. Algebra, 18 (1971). | MR 276262 | Zbl 0231.16016
[8] , Lectures on Injective Modules and Quotient Rings, Lecture Notes in Math. 49 (1967). | MR 227206 | Zbl 0162.05002
[9] and , Direct sum representations of injective modules, J. ALGEBRA 5 (1967). | MR 207760 | Zbl 0173.03203
[10] , Sommes directes de sous-modules co-irréductibles d'un module, Math. Z. 103 (1968). | MR 225808 | Zbl 0155.07501
[11] , Abelian categories, New York, Harper and Row, 1964. | MR 166240 | Zbl 0121.02103
[12] , On quasi-injective modules, Annali della Scuola Norm. Sup. Pisa, 23 (1969). | Numdam | MR 258873 | Zbl 0191.03803
[13] and , Spektralkategorien und regulare Rings in Von Neumann Sinn, Math. Z. 92 (1966). | MR 225848 | Zbl 0136.25602
[14] and , Caractérisation des catégories abéliennes avec générateurs et limites inductives exactes, C.R. Acad. Sci. Paris, 258 (1964). | Zbl 0126.03304
[15] , Torsion-Free modules and rings, J. Algebra, 1 (1964). | MR 164991 | Zbl 0145.26804
[16] , On semi-simple abelian categories , Univ. de Buenos Aires (Osaka J. Math. 5 (1968)). | MR 252477 | Zbl 0181.03001
[17] , and , On categories of indecomposable modules I, Osaka J. Math. 7 (1970). | MR 286859 | Zbl 0248.18018
[18] , On categories of indecomposable modules II, Osaka J. Math. 8 (1971). | MR 304431 | Zbl 0248.18019
[19] and , On categories of projective modules, Osaka J. Math., 9 (1971). | MR 318223 | Zbl 0262.16030
[20] , Supplementary remarks on categories of indecomposable modules, Osaka J. Math. 9 (1972). | MR 304432 | Zbl 0262.16031
[21] , Note on categories of indecomposable modules, Pub. Math. Univ. Lyon. T. 9. (1972). | Numdam | MR 338076 | Zbl 0303.16014
[22] , On perfect categories I~IV, Osaka J. Math. 10 (1973). | MR 367017 | Zbl 0293.18014
[23] and , Self-injective rings, Can. Math. Bull. 2 (1969). | MR 106922 | Zbl 0090.25202
[24] , Note on Krull-Remak-Schmidt-Azumaya' theorem, Osaka J. Math. 9 (1972). | Zbl 0251.16019
[25] , Problem of Krull-Remak-Schmidt-Azumaya-Matlis, J. Indian Math. Soc. 35 (1971). | MR 306262 | Zbl 0267.16013
[26] , Projective modules, Ann. of Math. 68 (1958). | MR 100017 | Zbl 0083.25802
[27] , On the radical of a category, J. Austral.Math. Soc. 4 (1964). | MR 170922 | Zbl 0124.01501
[28] , Semi-perfect modules, Math. Z. 83 (1963). | MR 157985 | Zbl 0131.27401
[29] , Injectives modules over noetherian rings, Pacific J. Math. 8 (1958). | MR 99360 | Zbl 0084.26601
[30] , Theory of categories, Academic Press, 1965. | MR 202787 | Zbl 0136.00604
[31] , Quasi-injective modules, Perfect modules and a theorem for modular lattices, J. Fac. Sci. Hokkaido Univ. 12 (1966). | MR 213390 | Zbl 0142.27904
[32] , On algebraically closed modules, Publ. Math. Debrecen 6 (1959). | MR 121390 | Zbl 0090.02405
[33] , On the radical of rings of row-finite matrices, Proc. Royal Soc. Edinburgh 66 (1962). | MR 142582 | Zbl 0145.27103
[34] , Lectures on Rings and Modules (Closure Spaces with Applications to Ring Theory), Lecture Notes in Math. 246 Springer-Verlag. | MR 371787 | Zbl 0229.16019
[35] , On regular categories, Osaka J. Math. 7 (1970). | MR 276300 | Zbl 0261.18009
[36] and , The radical of the row-finite matrices over an arbitrary ring, Trans. Amer. Math. Soc. 139 (1965). | MR 238889 | Zbl 0191.31803
[37] and , The radical of the endomorphism ring of a projective modules, Proc. Amer. Math. Soc. 26 (1970). | MR 262281 | Zbl 0204.36301
[38] , A Krull-Remak-Schmidt theorem for infinite sums of modules, Proc. Amer. Math. Soc. 22 (1969). | MR 242886 | Zbl 0176.31401
[39] , Decomposition of injective modules, Pacific J. Math. 31 (1969). | MR 249467 | Zbl 0185.04102
[40] , Non-singular and Matlis'problem, Sci. Rep. Tokyo Kyoiku-Daigaku, 11 (1972). | MR 314905 | Zbl 0265.16015
[41] , A note on a Problem of Matlis, Proc Japan Acad. Sci. 49 (1973). | MR 396670 | Zbl 0276.16024
[42] , Completely decomposable modules which have the exchange property, to appear.