Skip to main content Accessibility help
×
Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-12-02T18:18:36.265Z Has data issue: false hasContentIssue false

Local-global principles and approximation theorems

Published online by Cambridge University Press:  30 March 2017

Ali Enayat
Affiliation:
American University, Washington DC
Iraj Kalantari
Affiliation:
Western Illinois University
Mojtaba Moniri
Affiliation:
Tarbiat Modares University, Tehran, Iran
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Logic in Tehran , pp. 114 - 125
Publisher: Cambridge University Press
Print publication year: 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] J.-L., Colliot-Thélène, The Hasse principle in a pencil of algebraic varieties,Number Theory (Tiruchirapalli, 1996), Contemporary Mathematics, vol. 210, AMS, Providence, RI, 1998, pp. 19–39.
[2] L., Darnière, Decidability and local-global principles,Hilbert's Tenth Problem: Relations With Arithmetic and Algebraic Geometry (Ghent, 1999), Contemporary Mathematics, vol. 270, AMS, Providence, RI, 2000, pp. 145–167.
[3] Yu. L., Ershov, Multiple valued fields,Russian Mathematical Surveys, vol. 37 (1982), no. 3, pp. 63–107.
[4] Yu. L., Ershov, Two theorems on regularly r-closed fields,Journal fur die Reine und Angewandte Mathematik, vol. 347 (1984), pp. 154–167.Google Scholar
[5] Yu. L., Ershov, Relative regular closeness and π-valuations,Algebra and Logic, vol. 31 (1992), no. 6, pp. 342–360.Google Scholar
[6] Yu. L., Ershov, On surprising (wonderful) extensions of the field of rationals,Rossiıskaya Akademiya Nauk. Doklady Akademii Nauk, vol. 62 (2000), no. 1, pp. 8–9.Google Scholar
[7] Yu. L., Ershov, Multi-Valued Fields, Kluwer Academic/Plenum Publishers, 2001.
[8] Yu. L., Ershov, Preordered multivalued fields,Rossiıskaya Akademiya Nauk. Doklady Akademii Nauk, vol. 65 (2002), no. 1, pp. 75–79.Google Scholar
[9] Yu. L., Ershov, Nice extensions and global class field theory,Rossiıskaya Akademiya Nauk. Doklady Akademii Nauk, vol. 67 (2003), no. 1, pp. 21–23.Google Scholar
[10] B., Green, F., Pop, and P., Roquette, On Rumely's local-global principle,Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 97 (1995), no. 2, pp. 43–74.Google Scholar
[11] C., Grob, Die Entscheidbarkeit der Theorie der maximalen pseudo-p-adisch abgeschlossenen Körper, Dissertation, Universitat Konstanz, 1987.
[12] B., Heinemann and A., Prestel, Fields regularly closed with respect to finitely many valuations and orderings,Quadratic and Hermitian Forms (Hamilton, Ont., 1983), CMS Conf. Proc., vol. 4, AMS, Providence, RI, 1984, pp. 297–336.
[13] M., Jarden, Algebraic realization of p-adically projective groups,Compositio Mathematica, vol. 79 (1991), no. 1, pp. 21–62.Google Scholar
[14] L., Moret-Bailly, Groupes de Picard et problèmes de Skolem. I, II,Annales Scientifiques de l'É cole Normale Superieure. Quatrieme Serie, vol. 22 (1989), no. 2, pp. 161–179, 181–194.Google Scholar
[15] A., Prestel, Pseudo real closed fields,Set Theory and Model Theory (Bonn, 1979), Lecture Notes in Mathematics, vol. 872, Springer, Berlin, 1981, pp. 127–156.
[16] R., Rumely, Arithmetic over the ring of all algebraic integers,Journal fur die Reine und Angewandte Mathematik, vol. 368 (1986), pp. 127–133.Google Scholar
[17] J., Schmid, Regularly T-closed fields,Hilbert's Tenth Problem: Relations with Arithmetic and Algebraic Geometry (Ghent, 1999), Contemporary Mathematics, vol. 270, AMS, Providence, RI, 2000, pp. 187–212.
[18] L., van den Dries, Model Theory of Fields, Thesis, Utrecht, 1978.
[19] O., Zariski and P., Samuel, Commutative Algebra. Vol. II, D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-London-New York, 1960.

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×