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Structure of additive categories. (English) Zbl 0365.18014

MSC:

18E05 Preadditive, additive categories
16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras
16Kxx Division rings and semisimple Artin rings
16D90 Module categories in associative algebras
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References:

[1] 1 Behrens E.A. , Algebren , BI-Hochschultaschenbuch , Frankfurt /M., 1965 . MR 225806
[2] 2 Dartois G. , Catégories préadditives et modules , Esquisses Math. 13 , Paris ( 1971 ). MR 435179 | Zbl 0374.18007 · Zbl 0374.18007
[3] 3 Faith C. , Algebra: Rings, modules, categories I , Springer , 1970 , Berlin . MR 366960 | Zbl 0508.16001 · Zbl 0508.16001
[4] 4 Gabriel-Ulmer , Lokal präsentierbare Kategorien , Lecture Notes in Math . 221 ( 1971 ). Zbl 0225.18004 · Zbl 0225.18004 · doi:10.1007/BFb0059396
[5] 5 Harari S. , Pureté et platitude dans les catégories de foncteurs , Esquisses Math. 11 , Paris ( 1971 ). MR 414650 | Zbl 0403.18001 · Zbl 0403.18001
[6] 6 Jacobson N. , Structure of rings , Providence , 1964 . MR 222106 · Zbl 0117.03301
[7] 7 Kelly M. , On the radical of a category , J. Austral. Math. Soc. 4 ( 1964 ). MR 170922 | Zbl 0124.01501 · Zbl 0124.01501 · doi:10.1017/S1446788700024071
[8] 8 Lambek J. Lectures on rings and modules , Blaisd. , Toronto , 1966 . MR 206032 | Zbl 0143.26403 · Zbl 0143.26403
[9] 9 Lambek J. , Torsion theories, additive semantics and rings of quotients , Lecture Notes in Math . 177 ( 1971 ). MR 284459 | Zbl 0213.31601 · Zbl 0213.31601
[10] 10 Leduc P.Y. , Catégories semi-simples et catégories primitives , Can. J. Math. 20 ( 1968 ). MR 228568 | Zbl 0159.02104 · Zbl 0159.02104 · doi:10.4153/CJM-1968-060-7
[11] 11 Leduc P.Y. , Radical et primitivité des catégories , Cahiers Topo. et Géo. diff. X - 3 ( 1968 ). Numdam | MR 242927 | Zbl 0183.30302 · Zbl 0183.30302
[12] 12 Mitchell B. , Theory of categories , A. P. , New-York , 1965 . MR 202787 | Zbl 0136.00604 · Zbl 0136.00604
[13] 13 Mitchell B. , Rings with several objects , Adv. in Math. 8 ( 1970 ). MR 294454 | Zbl 0232.18009 · Zbl 0232.18009 · doi:10.1016/0001-8708(72)90002-3
[14] 14 Popescu N. , Abelian categories with applications to rings and modules , A. P. , New-York , 1973 . MR 340375 | Zbl 0271.18006 · Zbl 0271.18006
[15] 15 Schubert H. , Categories , Springer , Berlin , 1972 . Zbl 0253.18002 · Zbl 0253.18002
[16] 16 Suzuki Y. , Dominant dimension of double centralizers , Math. Zeit. 122 ( 1971 ). Article | MR 289582 | Zbl 0226.16033 · Zbl 0226.16033 · doi:10.1007/BF01113563
[17] 17 Weidenfeld G. , Objets injectifs et catégories de fractions , Esquisses Math. 3 , Paris ( 1970 ). MR 419560 | Zbl 0377.18004 · Zbl 0377.18004
[18] 18 Weidenfeld M. , Idéaux d’une catégorie préadditive , Esquisses Math. 3 , P a-ris ( 1970 ). · Zbl 0377.18005
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