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Problems in the arithmetic of fields and Galois theory. (Problèmes d’arithmétique des corps et de théorie de Galois.) (French) Zbl 0912.12001

Collection Méthodes. Paris: Hermann. 248 p. (1998).
The aim of this book is two-fold: first, to present some well-known facts in the arithmetic of fields and Galois theory, including: polynomials and cyclotomic fields, finite fields, the quadratic reciprocity law, the fundamental theorem of algebra, the four squares theorem, etc., and second, to discuss more special topics, including skew fields, inverse Galois theory, differential fields, ordered fields, etc.
This is a very nice book, very carefully written, with complete proofs of the results presented and complete solutions of the exercises, covering in few pages a large spectrum of an interesting topic in field theory. The book is recommended to graduates students, and to anyone wishing to enlarge his/her standard knowledge in this beautiful area of algebra and number theory, as well.

MSC:

12-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to field theory
12E20 Finite fields (field-theoretic aspects)
12F10 Separable extensions, Galois theory
00A07 Problem books
12E15 Skew fields, division rings
12J15 Ordered fields
12F12 Inverse Galois theory
12H05 Differential algebra
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