On the Theory of Radicals in a Ring

Masayoshi NAGATA

doi:10.2969/jmsj/00320330

Masayoshi NAGATA

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ジャーナルフリー

1951 年 3 巻 2 号 p. 330-344

DOI https://doi.org/10.2969/jmsj/00320330

詳細

Published: 1951 Received: 1950/07/12 Available on J-STAGE: 2006/08/29 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/08/29 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Right : 1. G. Azumaya, On generalized semi-primary rings and Krull-Remak-Schmidt's theorem, Jap. J. Math. vol. 19 (1948) pp. 525-547.
2. R. Baer, Radical ideals, Amer. J. Math. vol. 65 (1943) pp. 537-568.
3. B. Brown and N. H. McCoy, Rings with unit element which contain a given ring, Duke Math. vol. 13 (1946) pp. 9-20.
4. B. Brown and N. H. McCoy, Radicals and subdirect sums, Amer. J, Math. vol. 67 (1947) pp. 46-58.
5. H. Fitting, Primärkomponentenzerlegung in nichtkommutativen Ringe, Math. Ann. vol. 111 (1935) pp. 19-41.
6. N. Jacobson, The radical and semi-simplicity for arbitrary rings, Amer. J. Math. vol. 76 (1945) pp. 300-320.
7. N. Jacobson, Structure theory of simple rings without finiteness assumption, Trans. Amer. Math. Soc, vol. 57 (1945) pp. 228-245.
8. N. Jacobson, On the theory of primitive rings, Ann. Math. vol. 48 (1947).
9. G. Köthe, Die Strukture der Ringe deren Restklassenring nach den Radikal vollstandig reduzibel ist, Math. Zeit, vol. 32 (1930) pp. 161-186.
10. J. Levitzki, On the radical of a ring, Bull. Amer. Math. Soc. vol. 49 (1943) pp. 462-466.
11. J. Levitzki, On three problems concerning nil-rings, Bull. Amer. Math. Soc. vol. 51 (1945) pp. 913-919.
12. N. H. McCoy, Prime ideals in general rings, Amer. J. Math. vol. 71 (1949) pp. 833-833.
13. T. Nakayama, Uber Einfache distributive Systeme unendlicher Range, Proc. Imp. Acad. Tokyo vol. 20 (1944) pp. 61-66.
14. T. Nakayama, Note on irreducible ring, to appear in Proc. Jap. Acad..
15. T. Nakayama and G. Azumaya, On irreducible rings, Ann. Math. vol. 48 (1947) pp. 949-965.
16. S. Perlis, A characterization of radical of an algebra, Bull. Amer. Math Soc. vol. 48 (1942) pp. 128-132.

訂正日: 2006/08/29 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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