Strong approximation theorem for division algebras over R(X)
ジャーナル
フリー
1997 年 49 巻 3 号 p. 455-467
詳細
- Published: 1997 Received: 1995/05/31 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
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訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文タイトル 訂正内容: Wrong : Strong approximation theorem for division algebras over R(X)
Right : Strong approximation theorem for division algebras over R(X)
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報 訂正内容: Wrong : 1) A. Albert, Structure of algebras, Amer. Math. Soc. Colloq. Publ., 24 (1939).
2) M. Auslander and A. Brumer, Brauer groups of discrete valuation rings, Nederl. Akad. Wetensch. Proc. Ser. A, 71 (1968), 286-296.
3) C. W. Curtis and I. Reiner, Methods of representation theory, vol. 1, vol. 2. Interscience (1981, 1987). Especially §23 lattices and orders, §51 Jacobinski's cancellation theorem.
4) D. K. Faddeev, Simple algebras over a field of algebraic functions of one variable. Amer. Math. Soc. Transl. Ser. II, 3 (1956), 15-38.
5) B. Fein and M. Schacher, Brauer groups of rational function fields over global fields. Springer, Lecture Notes in Math., 844 (1981), 46-74.
6) H. Hijikata, On the decomposition of lattices over orders, to appear in this issue.
7) A. Pfister, Zur Darstellung definiter Funktionen als Summe von Quadraten, Invent. Math., 4 (1967), 229-237.
8) V. P. Platonov, The Tannaka-Artin problem and reduced K-theory, Math. USSR. Izvestija, 10 (1976), 211-243.
9) W. Scharlau, Quadratic and Hermitian forms, Springer, GMW, 270 (1985).
10) J. P. Serre, Corps locaux, Hermann (1968).
11) R. G. Swan, Strong approximation and locally free modules, Ring Theory and Algebra III (B. McDonald, ed.), Marcel Dekker, New York, (1980), 153-223.
Right : [1] A. Albert, Structure of algebras, Amer. Math. Soc. Colloq. Publ., 24 (1939).
[2] M. Auslander and A. Brumer, Brauer groups of discrete valuation rings, Nederl. Akad. Wetensch. Proc. Ser. A, 71 (1968), 286-296.
[3] C. W. Curtis and I. Reiner, Methods of representation theory, vol. 1, vol. 2. Interscience (1981, 1987). Especially §23 lattices and orders, §51 Jacobinski's cancellation theorem.
[4] D. K. Faddeev, Simple algebras over a field of algebraic functions of one variable. Amer. Math. Soc. Transl. Ser. II, 3 (1956), 15-38.
[5] B. Fein and M. Schacher, Brauer groups of rational function fields over global fields. Springer, Lecture Notes in Math., 844 (1981), 46-74.
[6] H. Hijikata, On the decomposition of lattices over orders, to appear in this issue.
[7] A. Pfister, Zur Darstellung definiter Funktionen als Summe von Quadraten, Invent. Math., 4 (1967), 229-237.
[8] V. P. Platonov, The Tannaka-Artin problem and reduced K-theory, Math. USSR. Izvestija, 10 (1976), 211-243.
[9] W. Scharlau, Quadratic and Hermitian forms, Springer, GMW, 270 (1985).
[10] J. P. Serre, Corps locaux, Hermann (1968).
[11] R. G. Swan, Strong approximation and locally free modules, Ring Theory and Algebra III (B. McDonald, ed.), Marcel Dekker, New York, (1980), 153-223.
訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル 訂正内容: -
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