Strong approximation theorem for division algebras over R(X)

Aiichi YAMASAKI

doi:10.2969/jmsj/04930455

Aiichi YAMASAKI

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JOURNAL FREE ACCESS

1997 Volume 49 Issue 3 Pages 455-467

DOI https://doi.org/10.2969/jmsj/04930455

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Published: 1997 Received: May 31, 1995 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: TITLE Details: Wrong : Strong approximation theorem for division algebras over R(X)
Right : Strong approximation theorem for division algebras over R(X)

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: 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.

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