Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 1145.12001
Fried, Michael D.; Jarden, Moshe
Field arithmetic. Revised by Moshe Jarden. 3rd revised ed. (English)
[B] Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge 11. Berlin: Springer. xxiv, 792~p. EUR~171.15; SFR~278.00 (2008). ISBN 978-3-540-77269-9/hbk

The third edition of this widely appreciated book appears only three years later than the second edition. We refer to Zbl 0625.12001 and Zbl 1055.12003 for comments to the first two editions. This new edition improves on the previous edition in two ways: first, it removes a number of mathematical inaccuracies and typos, including three or four pages of missing references; second, it reports on five open problems of the second edition which have been solved since. We list the problems solved (or partially solved), with reference to the solution: Problems~2 and~3: {\it J. Kollár} [Isr. J. Math. 161, 89--101 (2007; Zbl 1143.12003), Theorems~1 and~2]; Problem~3: {\it J. Kollár} [Isr. J. Math. 162, 235--251 (2007; Zbl 1140.14009), Theorem 1]; Problem~31: {\it L. Bary-Soroker} [Math. Ann. 336, No. 4, 949--961 (2006; Zbl 1111.20029)]; Problem~33: the solution comes from a reorganization of the proof of Corollary 28.5.3 suggested by E. Rosen. At the end of the book a new selection of open problems is included.
[Roberto Dvornicich (Pisa)]

MSC 2000:: *12E30 Field arithmetic
12-02 Research monographs (field theory)
12E25 Hilbertian fields; Hilbert's irreducibility theorem
12F12 Inverse Galois theory
12Lxx Connections of field theory with logic
14G05 Rationality questions, rational points

Keywords: field arithmetic; Hilbertian fields

Citations: Zbl 0625.12001; Zbl 1055.12003; Zbl 1140.14009; Zbl 1111.20029; Zbl 1143.12003

Cited in: Zbl 1235.12002

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]