LEADER 03680nam 22005415 450 001 9910300106403321 005 20230711071255.0 010 $a3-319-95177-7 024 7 $a10.1007/978-3-319-95177-5 035 $a(CKB)4100000007110537 035 $a(DE-He213)978-3-319-95177-5 035 $a(MiAaPQ)EBC6314243 035 $a(PPN)232471444 035 $a(EXLCZ)994100000007110537 100 $a20181102d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAlgebra $eFrom the Viewpoint of Galois Theory /$fby Siegfried Bosch 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2018. 215 $a1 online resource (XV, 352 p. 13 illus.) 225 1 $aBirkhäuser Advanced Texts Basler Lehrbücher,$x2296-4894 311 $a3-319-95176-9 327 $aElementary Group Theory -- Rings and Polynomials -- Algebraic Field Extensions -- Galois Theory -- More on Group Theory -- Applications of Galois Theory -- Transcendental Field Extensions. 330 $aThe material presented here can be divided into two parts. The first, sometimes referred to as abstract algebra, is concerned with the general theory of algebraic objects such as groups, rings, and fields, hence, with topics that are also basic for a number of other domains in mathematics. The second centers around Galois theory and its applications. Historically, this theory originated from the problem of studying algebraic equations, a problem that, after various unsuccessful attempts to determine solution formulas in higher degrees, found its complete clarification through the brilliant ideas of E. Galois. The study of algebraic equations has served as a motivating terrain for a large part of abstract algebra, and according to this, algebraic equations are visible as a guiding thread throughout the book. To underline this point, an introduction to the history of algebraic equations is included. The entire book is self-contained, up to a few prerequisites from linear algebra. It covers most topics of current algebra courses and is enriched by several optional sections that complement the standard program or, in some cases, provide a first view on nearby areas that are more advanced. Every chapter begins with an introductory section on "Background and Overview," motivating the material that follows and discussing its highlights on an informal level. Furthermore, each section ends with a list of specially adapted exercises, some of them with solution proposals in the appendix. The present English edition is a translation and critical revision of the eighth German edition of the Algebra book by the author. The book appeared for the first time in 1993 and, in later years, was complemented by adding a variety of related topics. At the same time it was modified and polished to keep its contents up to date. 410 0$aBirkhäuser Advanced Texts Basler Lehrbücher,$x2296-4894 606 $aAlgebraic fields 606 $aPolynomials 606 $aGeometry, Algebraic 606 $aField Theory and Polynomials 606 $aAlgebraic Geometry 615 0$aAlgebraic fields. 615 0$aPolynomials. 615 0$aGeometry, Algebraic. 615 14$aField Theory and Polynomials. 615 24$aAlgebraic Geometry. 676 $a512.32 700 $aBosch$b Siegfried$4aut$4http://id.loc.gov/vocabulary/relators/aut$041946 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300106403321 996 $aAlgebra$91101347 997 $aUNINA