Algebra. Volume I: Fields and Galois theory. Translated from the 1987 German edition by Silvio Levy. With the collaboration of the translator
type: Item
instance of: scholarly article
title: Algebra. Volume I: Fields and Galois theory. Translated from the 1987 German edition by Silvio Levy. With the collaboration of the translator
zbMATH Open document ID: 1087.12001
DOI: 10.1007/0-387-31608-6
author: Falko Lorenz
published in: Universitext
publication date: 2006-03-16T00:00:00Z
review text: This is the faithful English translation of the German textbook ``Einführung in die Algebra: Teil I'' by F. Lorenz, the first edition of which appeared in 1987 (Zbl 0639.12008). Due to its special character, this introduction to classical abstract algebra quickly became one of the most popular texts on the subject for advanced undergraduate students at German-language universities, and thus its second, slightly revised edition came out already five years later (1992). Now, almost twenty years after the appearance of the German original, the well-deserved English edition of this outstanding textbook has been brought about by Springer Verlag, with some further improvements and (finally) in modern printing. In view of the fact that there is certainly no lack of excellent introductions to topics of abstract algebra, it ought to be explained what the peculiar features of the textbook under review actually are. As the author points out in the preface, this text is to provide a lively, problem-oriented, comprehensible, but nevertheless profound introduction to those concepts and methods of modern abstract algebra that are related to field extensions and classical Galois theory, thereby assuming no more prerequisites than the basics of linear algebra. In this vein, the author sets a high value on both motivating concrete problems and detailed explanations of the theoretical framework for tackling them. Following this didactical principle, the author develops the conceptual tools gradually as needed, thereby avoiding the more or less usual, systematic, but somewhat dry standard style of many other, admittedly more encyclopedic textbooks on the subject. Despite its pronounced didactical touch, the text leads the reader right away into depth, and the author offers quite a number of interesting methodological approaches, extra topics, and arithmetical applications. As to the contents of this first volume of the author's introduction to algebra, the text consists of 19 sections …
reviewed by: Werner Kleinert
Mathematics Subject Classification ID: 12Exx
Mathematics Subject Classification ID: 12-01
Mathematics Subject Classification ID: 12Fxx
Mathematics Subject Classification ID: 00-01
Mathematics Subject Classification ID: 13-01
Mathematics Subject Classification ID: 20-01
Mathematics Subject Classification ID: 11Txx
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 5012869
zbMATH Keywords: textbook
zbMATH Keywords: algebraic structures
zbMATH Keywords: fields
zbMATH Keywords: algebraic equations
zbMATH Keywords: Galois theory
zbMATH Keywords: rings
zbMATH Keywords: groups
zbMATH Keywords: algebras
zbMATH Keywords: algebraic number theory
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/0-387-31608-6
OpenAlex ID: W4234441230
description: scientific article; zbMATH DE number 5012869