Beschreibung
The central theme of the book is the study of algebraic equations and their corresponding field extensions, enriched by some more advanced topics that are optional. In particular, the author discuss the basics on finite and algebraic extensions, on separable and purely inseparable extensions, as well as on splitting fields and the construction of algebraic closures. On a second stage, he gives a comprehensive account on Galois theory, including the key techniques necessary for characterizing the solvability of algebraic equations via their corresponding Galois groups. There are some further applications of Galois theory, like a proof of the Fundamental Theorem of Algebra, a discussion of compass and straightedge constructions, as well as the explicit solution formulas for algebraic equations of degrees 3 and 4 from the 16th century. Furthermore, the author has included a historical introduction to the problem of solving algebraic equations at the very beginning of the book. Whenever appropriate chapters are enriched by additional material that leads to a deeper understanding of the subject. The whole text is self-contained, up to a few rudimentary facts from Linear Algebra. Each chapter of the book starts with a motivating introduction entitled "Background and Overview", which contains an informal discussion of the subjects dealt with in subsequent sections. All sections end with a list of specially adapted exercises, some of them with solutions in the Appendix. The book is an English translation and revision of the eighth edition of my German book on Algebra. The latter appeared for the first time in 1993 and, in later years, was modified and polished substantially in order to present things in a way as simple as possible, however, without resorting to simplifying and inappropriate ad hoc solutions.
Autorenporträt
Siegfried Bosch, Universität Münster, Germany.
Herstellerkennzeichnung:
Springer Basel AG in Springer Science + Business Media
Heidelberger Platz 3
14197 Berlin
DE
E-Mail: juergen.hartmann@springer.com
