Topics in field theory. (English) Zbl 0662.12023

North-Holland Mathematics Studies, 155; Notas de Matemática, 124. Amsterdam etc.: North-Holland. xi, 546 p. $ 144.75; Dfl. 275.00 (1989).
This book deals with selected topics from the theory of fields, as the title so aptly describes. The contents of the book are fairly basic. For the most part, the reader needs only have had the equivalent of a first- year graduate course in abstract algebra. The topics the author has chosen to include are quite interesting. He has nicely woven together classical results with contemporary ones. Many of the works have never appeared in book form before. For example, the author has included the pioneering work of S. MacLane on separable field extensions and the recent important works of W. Waterhouse and R. Rasala on purely inseparable field extensions. Some of the topics included in the book are separable extensions, transcendental extensions, derivations, purely inseparable extensions, Galois theory, abelian extensions, and radical extensions. Due to space constraints, there are relevant recent results on fields which do not appear in the book. However the author has an extensive bibliography which covers most of them.
Reviewer: J.N.Mordeson


12Fxx Field extensions
12-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to field theory
12F10 Separable extensions, Galois theory
12F15 Inseparable field extensions
12F20 Transcendental field extensions