Applications of Factor Categories to Completely Indecomposable Modules
Publications du Département de mathématiques (Lyon), Tome 11 (1974) no. 2, pp. 19-104.
@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)},
     pages = {19--104},
     publisher = {Universit\'e Claude Bernard - Lyon 1},
     volume = {11},
     number = {2},
     year = {1974},
     zbl = {0335.13006},
     mrnumber = {364356},
     language = {en},
     url = {http://www.numdam.org/item/PDML_1974__11_2_19_0/}
}
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Harada, Manabu. Applications of Factor Categories to Completely Indecomposable Modules. Publications du Département de mathématiques (Lyon), Tome 11 (1974) no. 2, pp. 19-104. http://www.numdam.org/item/PDML_1974__11_2_19_0/

[1] G. Azumaya, Correction and supplementaires to my paper concering Krull-Remak-Schmidt'theorem, Nagoya Math. J. 1 (1950). | MR 37832 | Zbl 0040.01201

[2] H. Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960). | MR 157984 | Zbl 0094.02201

[3] S.U. Chase, Direct products of modules, Trans. Amer. Math. Soc. 97 (1960). | MR 120260 | Zbl 0100.26602

[4] P. Crawley and B. Jonnson, Refinements for infinite direct decomposition of algebraic system, Pacific J. Math. 14 (1964). | MR 169806 | Zbl 0134.25504

[5] C. Ehresmann, Catégories et structures, Dunod, Paris, 1965. | MR 213410 | Zbl 0136.25801

[6] S. Elliger, Zu dem Satz von Krull-Remak-Schmidt-Azumaya, Math. Z. 115 (1970). | MR 269687 | Zbl 0188.09001

[7] S. Elliger, Interdirekte Summen von Moduln, J. Algebra, 18 (1971). | MR 276262 | Zbl 0231.16016

[8] C. Faith, Lectures on Injective Modules and Quotient Rings, Lecture Notes in Math. 49 (1967). | MR 227206 | Zbl 0162.05002

[9] C. Faith and E.A. Walker, Direct sum representations of injective modules, J. ALGEBRA 5 (1967). | MR 207760 | Zbl 0173.03203

[10] J. Fort, Sommes directes de sous-modules co-irréductibles d'un module, Math. Z. 103 (1968). | MR 225808 | Zbl 0155.07501

[11] P. Freyd, Abelian categories, New York, Harper and Row, 1964. | MR 166240 | Zbl 0121.02103

[12] L. Fuchs, On quasi-injective modules, Annali della Scuola Norm. Sup. Pisa, 23 (1969). | Numdam | MR 258873 | Zbl 0191.03803

[13] P. Gabriel and U. Oberst, Spektralkategorien und regulare Rings in Von Neumann Sinn, Math. Z. 92 (1966). | MR 225848 | Zbl 0136.25602

[14] P. Gabriel and N. Popescu, Caractérisation des catégories abéliennes avec générateurs et limites inductives exactes, C.R. Acad. Sci. Paris, 258 (1964). | Zbl 0126.03304

[15] A. W. Goldie, Torsion-Free modules and rings, J. Algebra, 1 (1964). | MR 164991 | Zbl 0145.26804

[16] M. Harada, On semi-simple abelian categories , Univ. de Buenos Aires (Osaka J. Math. 5 (1968)). | MR 252477 | Zbl 0181.03001

[17] M. Harada, and Y. Sai, On categories of indecomposable modules I, Osaka J. Math. 7 (1970). | MR 286859 | Zbl 0248.18018

[18] M. Harada, On categories of indecomposable modules II, Osaka J. Math. 8 (1971). | MR 304431 | Zbl 0248.18019

[19] M. Harada and H. Kanbara, On categories of projective modules, Osaka J. Math., 9 (1971). | MR 318223 | Zbl 0262.16030

[20] M. Harada, Supplementary remarks on categories of indecomposable modules, Osaka J. Math. 9 (1972). | MR 304432 | Zbl 0262.16031

[21] M. Harada, Note on categories of indecomposable modules, Pub. Math. Univ. Lyon. T. 9. (1972). | Numdam | MR 338076 | Zbl 0303.16014

[22] M. Harada, On perfect categories I~IV, Osaka J. Math. 10 (1973). | MR 367017 | Zbl 0293.18014

[23] R.E. Johnson and E.T. Wong, Self-injective rings, Can. Math. Bull. 2 (1969). | MR 106922 | Zbl 0090.25202

[24] K. Kanbara, Note on Krull-Remak-Schmidt-Azumaya' theorem, Osaka J. Math. 9 (1972). | Zbl 0251.16019

[25] U.S. Kahlon, Problem of Krull-Remak-Schmidt-Azumaya-Matlis, J. Indian Math. Soc. 35 (1971). | MR 306262 | Zbl 0267.16013

[26] I. Kaplansky, Projective modules, Ann. of Math. 68 (1958). | MR 100017 | Zbl 0083.25802

[27] G.M. Kelly, On the radical of a category, J. Austral.Math. Soc. 4 (1964). | MR 170922 | Zbl 0124.01501

[28] E. Mares, Semi-perfect modules, Math. Z. 83 (1963). | MR 157985 | Zbl 0131.27401

[29] E. Matlis, Injectives modules over noetherian rings, Pacific J. Math. 8 (1958). | MR 99360 | Zbl 0084.26601

[30] B. Mitchell, Theory of categories, Academic Press, 1965. | MR 202787 | Zbl 0136.00604

[31] Y. Miyashita, Quasi-injective modules, Perfect modules and a theorem for modular lattices, J. Fac. Sci. Hokkaido Univ. 12 (1966). | MR 213390 | Zbl 0142.27904

[32] Z. Papp, On algebraically closed modules, Publ. Math. Debrecen 6 (1959). | MR 121390 | Zbl 0090.02405

[33] E.M. Patterson, On the radical of rings of row-finite matrices, Proc. Royal Soc. Edinburgh 66 (1962). | MR 142582 | Zbl 0145.27103

[34] R.S. Pierce, 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] Y. Sai, On regular categories, Osaka J. Math. 7 (1970). | MR 276300 | Zbl 0261.18009

[36] N.E. Sexauer and J.E. Warnock, The radical of the row-finite matrices over an arbitrary ring, Trans. Amer. Math. Soc. 139 (1965). | MR 238889 | Zbl 0191.31803

[37] R. Ware and J. Zelmanowitz, The radical of the endomorphism ring of a projective modules, Proc. Amer. Math. Soc. 26 (1970). | MR 262281 | Zbl 0204.36301

[38] R.B. Warfield Jr., A Krull-Remak-Schmidt theorem for infinite sums of modules, Proc. Amer. Math. Soc. 22 (1969). | MR 242886 | Zbl 0176.31401

[39] R.B. Warfield Jr., Decomposition of injective modules, Pacific J. Math. 31 (1969). | MR 249467 | Zbl 0185.04102

[40] K. Yamagata, Non-singular and Matlis'problem, Sci. Rep. Tokyo Kyoiku-Daigaku, 11 (1972). | MR 314905 | Zbl 0265.16015

[41] K. Yamagata, A note on a Problem of Matlis, Proc Japan Acad. Sci. 49 (1973). | MR 396670 | Zbl 0276.16024

[42] K. Yamagata, Completely decomposable modules which have the exchange property, to appear.