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Stable Extensions and Fields with the Global Density Property

Published online by Cambridge University Press:  20 November 2018

Michael Fried  and
Moshe Jarden
Michael Fried
Affiliation:
University of California at Irvine, Irvine, California
Moshe Jarden
Affiliation:
Tel-Aviv University, Ramat-Aviv, Tel-Aviv, Israel
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For a field M we denote by Ms and respectively the separable closure and the algebraic closure of M. If F is a variety which is defined over M, then we denote by V(M) the set of all if-rational points of V. M is said to be pseudo-algebraically closed (PAC) field, if V(M) ≠ θ for every non-void abstract variety V defined over M. It can be shown that then is dense in V(M) in the Zariski M -topology.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 4 , 01 August 1976 , pp. 774 - 787
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Cassels, J. W. S. and Frohlich, A., Algebraic number theory (Academic Press, London, 1967).Google Scholar
2. Chevalley, C., Introduction to the theory of algebraic functions of one variable (A.M.S., 1951).Google Scholar
3. Geyer, W. D. and Jarden, M., Fields with the density property, J. Algebra 35 (1975), 178–189.Google Scholar
4. Jarden, M., Elementary statements over large algebraic fields, Trans. Amer. Math. Soc. 164 (1972), 67–91.Google Scholar
5. Kuyk, W., Generic approach to the Galois embedding and extension problem, J. Algebra 9 (1968), 393–407.Google Scholar
6. Lang, S., Introduction to algebraic geometry (Interscience Publishers, New York, 1958).Google Scholar
7. Lang, S., Diophantine geometry (Interscience Publishers, New York, 1962).Google Scholar
8. Lang, S., Algebra (Addison-Wesley, Reading, Massachusetts, 1965).Google Scholar
9. Ribenboim, P., Théorie des valuations (Les Presses de l'Université de Montréal, Montréal, 1968).Google Scholar
10. Van, B. L. der Waerden, Modem Algebra, Vol. I (Springer, Berlin).Google Scholar
11. Weil, A., Foundations of algebraic geometry (A.M.S., Providence, 1962).Google Scholar
12. Zariski, O. and Samuel, P., Commutative algebra, Vol. II (Van Nostrand, Princeton, 1959).Google Scholar