On ruled fields
Journal de théorie des nombres de Bordeaux (1989)
- Volume: 1, Issue: 1, page 27-49
- ISSN: 1246-7405
Access Full Article
topAbstract
topHow to cite
topOhm, Jack. "On ruled fields." Journal de théorie des nombres de Bordeaux 1.1 (1989): 27-49. <http://eudml.org/doc/93499>.
@article{Ohm1989,
abstract = {Some results and problems that arise in connection with the foundations of the theory of ruled and rational field extensions are discussed.},
author = {Ohm, Jack},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {ruled field extension; uniruled; rational; unirational; subrational; subruled; ruled fields; ruling; generalized Lüroth theorem; Samuel problem; Zariski problem; separability},
language = {eng},
number = {1},
pages = {27-49},
publisher = {Université Bordeaux I},
title = {On ruled fields},
url = {http://eudml.org/doc/93499},
volume = {1},
year = {1989},
}
TY - JOUR
AU - Ohm, Jack
TI - On ruled fields
JO - Journal de théorie des nombres de Bordeaux
PY - 1989
PB - Université Bordeaux I
VL - 1
IS - 1
SP - 27
EP - 49
AB - Some results and problems that arise in connection with the foundations of the theory of ruled and rational field extensions are discussed.
LA - eng
KW - ruled field extension; uniruled; rational; unirational; subrational; subruled; ruled fields; ruling; generalized Lüroth theorem; Samuel problem; Zariski problem; separability
UR - http://eudml.org/doc/93499
ER -
References
top- [Am, 1955] S.A. Amitsur, Generic splitting fields of central simple algebras, Annals of Math.62 (1955), 8-43. Zbl0066.28604MR70624
- [A] E. Artin, Algebraic numbers and algebraic functions, Gordon and Breach, New-York (1967). Zbl0194.35301MR237460
- [BCSS, 1985] A. Beauville, J.-L. Colliot-Thelene, J.-J. Sansucand Sir Peter Swinnerton-Dyer, Variétés stablement rationnelles non rationnelles, Ann. of Math.121 (1986), 283- 318.. Zbl0589.14042MR786350
- [C, 1954] C. Chevalley, On algebraic group varieties, J. Math. Soc. Japan6 (1954), 305-324. Zbl0057.26301MR67122
- [D,1982] J. Deveney, Ruled function fields, Proc. Amer. Math. Soc.86 (1982), 213-215. Zbl0529.12016MR667276
- [E] O. Endler, Valuation theory, Springer Verlag, Heidelberg (1972). Zbl0257.12111MR357379
- [K, 1987] M. Kang, The biregular cancellation problem, J. of Pure and Applied Alg.45 (1987), 241-253. Zbl0639.13007MR890024
- [LT,1952] S. Lang and J. Tate, On Chevalley's proof of Lüroth's theorem, Proc. Amer. Math. Soc.3 (1952), 621-624. Zbl0047.03802MR49949
- [MH, 1982] T.T. Moh and W. Heinzer, On the Lüroth semigroups and Weierstrass canonical divisors, J. of Alg.7 (1982), 62-73. Zbl0533.14010MR665164
- [MB,1985] L. Moret-Bailly, Variétés stablement rationnelles non rationnelles, Séminaire Bourbaki (1984 -85). no 643, 14 pp. Zbl0605.14044
- [N,1967] M. Nagata, A theorem on valuation rings and its applications, Nagoya Math. J.29 (1967), 85-91. Zbl0146.26302MR207688
- [O, 1983] J. Ohm, The ruled residue theorem for simple transcendental extensions of valued fields, Proc. Amer. Math. Soc.89 (1983), 16-18. Zbl0523.12021MR706500
- [O, 1984] J. Ohm, On subfields of rational function fields, Arch. Math.42 (1984), 136-138. Zbl0546.12013MR751484
- [R, 1964] P. Roquette, Isomorphisms of generic splitting fields of simple algebras, J. Reine Angew. Math.214-215 (1964), 207-226. Zbl0219.16023MR166215
- [Sa, 1953] P. Samuel, Some remarks on Lüroth's theorem, Mem. Coll. Sci. Univ. Kyoto Ser. A. Math.27 (1953), 223-224. Zbl0053.01902MR58251
- [Sc] A. Schinzel, Selected topics on polynomials, Univ. of Mich. Press.Ann Arbor, 1982. Zbl0487.12002MR649775
- [Se, 1949] B. Segre, Sur un problème de M. Zariski, Coll. international d'algèbre et de théorie des nombres (Paris, 1949) 135-138. C.N.R.S., Paris, 1950 Zbl0040.08201MR41480
- [Sh] I.R. Shafarevich, Basic algebraic geometry, Grundlehren 213. Springer-Verlag, Heidelberg, 1974. Zbl0284.14001MR366917
- [vdW] B.L. van der WAERDEN, Modern Algebra, Unger. New-York, 1949. Zbl0039.00902
- [Wa,1975] W. Waterhouse, The structure of inseparable field extensions, Trans. Amer. Math. Soc.211 (1975), 39-56. Zbl0315.12101MR379454
- [W] A. Weil, Foundations of algebraic geometry, Coll. Pubs.XXIX, Amer. Math. Soc., Providence (1962). Zbl0168.18701MR144898
- [Z,1958] O. Zariski, On Castelnuovo's criterion of rationality pa = P2 = 0 of an algebraic surface, Illinois J. Math.2 (1958), 303-315. Zbl0085.36203MR99990
- [ZS 1] O. Zariski and P. Samuel, Commutative algebra. v. 1, van Nostrand, Princeton, 1958. Zbl0081.26501MR90581
- [ZS 2] O. Zariski and P. Samuel, Commutative algebra. v. 2, van Nostrand, Princeton, 1960. Zbl0121.27801MR120249
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.