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Titlebook: Algebra; From the Viewpoint o Siegfried Bosch Textbook 2018 Springer Nature Switzerland AG 2018 algebraic equation.field extension.algebrai

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发表于 2025-3-21 19:15:20 | 显示全部楼层 |阅读模式
期刊全称Algebra
期刊简称From the Viewpoint o
影响因子2023Siegfried Bosch
视频video
发行地址Combines the standard material on algebraic field extensions with some related but advanced topics.Each chapter starts with a motivating introduction and ends with a set of specially adapted exercises
学科分类Birkhäuser Advanced Texts‘ Basler Lehrbücher
图书封面Titlebook: Algebra; From the Viewpoint o Siegfried Bosch Textbook 2018 Springer Nature Switzerland AG 2018 algebraic equation.field extension.algebrai
影响因子.The 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 advan
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Praxis der Wirtschaftsinformatik was discovered that algebraic irrational numbers make up only a “very small” part of the realm of all irrational numbers, i.e., that most of them will not satisfy a nontrivial algebraic equation with coefficients in .. Such numbers were called ..
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1019-6242 roduction and ends with a set of specially adapted exercises.The 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
发表于 2025-3-22 19:12:17 | 显示全部楼层
Arbeitsebenen in FileMaker Pro, the problem that motivated E. Galois to work out his “Galois” theory. In particular, we show for a monic separable polynomial . with coefficients in a field . that the algebraic equation .(.) = 0 is solvable by radicals if and only if the corresponding Galois group is solvable in the group-theoretic sense.
发表于 2025-3-23 00:11:22 | 显示全部楼层
Applications of Galois Theory, the problem that motivated E. Galois to work out his “Galois” theory. In particular, we show for a monic separable polynomial . with coefficients in a field . that the algebraic equation .(.) = 0 is solvable by radicals if and only if the corresponding Galois group is solvable in the group-theoretic sense.
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发表于 2025-3-23 06:23:06 | 显示全部楼层
Elementary Group Theory,us, serving as a key tool for the investigation of algebraic equations. From a simplified point of view, Galois groups are permutation groups, i.e., groups whose elements describe bijective transformations (self-maps) on sets like {1, …, .}.
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