The Nullstellensatz over ℘-adically closed fields

Moshe JARDEN; Peter ROQUETTE

doi:10.2969/jmsj/03230425

Moshe JARDEN, Peter ROQUETTE

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ジャーナルフリー

1980 年 32 巻 3 号 p. 425-460

DOI https://doi.org/10.2969/jmsj/03230425

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Published: 1980 Received: 1978/07/25 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
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 : The Nullstellensatz over _??_-adically closed fields
Right : The Nullstellensatz over ℘-adically closed fields

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) S. Abhyankar, On the valuations centered in a local domain, Amer. J. Math., 78 (1956), 321-348.
2) J. Ax and S. Kochen, Diophantine problems over local fields I, II, Amer. J. Math., 87 (1965), 605-648; III, Ann. of Math., 83 (1966), 437-456.
3) S. A. Basarab, A model theoretic transfer theorem for Henselian valued fields, J. Reine Angew. Math., 311/312 (1979), 1-30.
4) O. Endler, Valuation theory, Springer, 1972.5a) Ju. L. Eršov, On elementary theories of maximal normed fields III (Russian), Algebra Logika Sem., 6, Nr. 3 (1967), 31-38.
5a) Ju. L. Eršov, On elementary theories of maximal normed fields III (Russian), Algebra Logika Sem., 6, Nr. 3 (1967), 31-38.
5b) Ju. L. Eršov, On rational points over Henselian fields (Russian), Algebra Logika Sem., 6, Nr. 3 (1967), 39-49.
6) I. Kaplansky, Commutative Rings, Boston, 1970.
7) J. J. Kelleher, Rings of meromorphic functions on non-compact Riemann surfaces, Canad. J. Math., 21 (1969), 284-300.
8) S. Kochen, Integer valued rational functions over the p-adic numbers: A p-adic analogue of the theory of real fields, Proc. Symp. Pure Math., 12, Number Theory, 57-73.
9) W. Krull, Jacobsonsche Ringe, Hilbertscher Nullstellensatz, Dimensionstheorie, Math. Zeitschr., 54 (1951), 354-387.
10) S. Lang, Some applications of the local uniformization theorem, Amer. J. Math., 76 (1954), 362-374.
11) M. Merckel, Wertbereiche rationaler Funktionen, Diplomarbeit, Heidelberg, 1975.
12) P. Roquette, Bemerkungen zur Theorie der formal p-adischen Körper, Beiträge z. Algebra u. Geometrie, 1 (1971), 177-193.
13) P. Roquette, Principal ideal theorems for holomorphy rings in fields, J. Reine Angew. Math., 262/263 (1973), 361-374.
14) P. Roquette, On the Riemann p-space of a field: The p-adic analogue of Weierstrass' approximation theorem and related problems, Abh. Math. Sem. Univ. Hamburg, 47 (1978), 236-259.
15) P. Roquette, A criterion for rational places over local fields, J. Reine Angew. Math., 292 (1977), 90-108.
16) R. Transier, Untersuchungen zu einer allgemeinen Theorie formal p-adischer Körper, Dissertation, Heidelberg, 1977.
17) V. Weispfenning, On the elementary theory of Hensel fields, Ann. Math. Logic, 10 (1976), 59-93.
18) V. Weispfenning, Nullstellensätze-A model theoretic framework, Z. Math. Logik Grundlagen Math., 23 (1977), 539-545.
19) O. Zariski, Local uniformization on algebraic varieties, Ann. of Math., ser. 2, 41 (1940), 852-896.
20) M. Ziegler, Die elementare Theorie der Henselschen Körper, Dissertation, Köln, 1972.
21) M. Ziegler, Nullstellensätze für lokale Körper, Mimeographed Notes.

Right : [1] S. Abhyankar, On the valuations centered in a local domain, Amer. J. Math., 78 (1956), 321-348.
[2] J. Ax and S. Kochen, Diophantine problems over local fields I, II, Amer. J. Math., 87 (1965), 605-648; III, Ann. of Math., 83 (1966), 437-456.
[3] S. A. Basarab, A model theoretic transfer theorem for Henselian valued fields, J. Reine Angew. Math., 311/312 (1979), 1-30.
[4] O. Endler, Valuation theory, Springer, 1972.
[5a] Ju. L. Eršov, On elementary theories of maximal normed fields III (Russian), Algebra Logika Sem., 6, Nr. 3 (1967), 31-38.
[5b] Ju. L. Eršov, On rational points over Henselian fields (Russian), Algebra Logika Sem., 6, Nr. 3 (1967), 39-49.
[6] I. Kaplansky, Commutative Rings, Boston, 1970.
[7] J. J. Kelleher, Rings of meromorphic functions on non-compact Riemann surfaces, Canad. J. Math., 21 (1969), 284-300.
[8] S. Kochen, Integer valued rational functions over the p-adic numbers: A p-adic analogue of the theory of real fields, Proc. Symp. Pure Math., 12, Number Theory, 57-73.
[9] W. Krull, Jacobsonsche Ringe, Hilbertscher Nullstellensatz, Dimensionstheorie, Math. Zeitschr., 54 (1951), 354-387.
[10] S. Lang, Some applications of the local uniformization theorem, Amer. J. Math., 76 (1954), 362-374.
[11] M. Merckel, Wertbereiche rationaler Funktionen, Diplomarbeit, Heidelberg, 1975.
[12] P. Roquette, Bemerkungen zur Theorie der formal p-adischen Körper, Beiträge z. Algebra u. Geometrie, 1 (1971), 177-193.
[13] P. Roquette, Principal ideal theorems for holomorphy rings in fields, J. Reine Angew. Math., 262/263 (1973), 361-374.
[14] P. Roquette, On the Riemann p-space of a field: The p-adic analogue of Weierstrass' approximation theorem and related problems, Abh. Math. Sem. Univ. Hamburg, 47 (1978), 236-259.
[15] P. Roquette, A criterion for rational places over local fields, J. Reine Angew. Math., 292 (1977), 90-108.
[16] R. Transier, Untersuchungen zu einer allgemeinen Theorie formal p-adischer Körper, Dissertation, Heidelberg, 1977.
[17] V. Weispfenning, On the elementary theory of Hensel fields, Ann. Math. Logic, 10 (1976), 59-93.
[18] V. Weispfenning, Nullstellensätze-A model theoretic framework, Z. Math. Logik Grundlagen Math., 23 (1977), 539-545.
[19] O. Zariski, Local uniformization on algebraic varieties, Ann. of Math., ser. 2, 41 (1940), 852-896.
[20] M. Ziegler, Die elementare Theorie der Henselschen Körper, Dissertation, Köln, 1972.
[21] M. Ziegler, Nullstellensätze für lokale Körper, Mimeographed Notes.

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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