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Titlebook: Introduction to the Galois Correspondence; Maureen H. Fenrick Textbook 1998Latest edition Springer Science+Business Media New York 1998 Ab

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書目名稱Introduction to the Galois Correspondence
編輯Maureen H. Fenrick
視頻videohttp://file.papertrans.cn/475/474359/474359.mp4
圖書封面Titlebook: Introduction to the Galois Correspondence;  Maureen H. Fenrick Textbook 1998Latest edition Springer Science+Business Media New York 1998 Ab
描述In this presentation of the Galois correspondence, modern theories of groups and fields are used to study problems, some of which date back to the ancient Greeks. The techniques used to solve these problems, rather than the solutions themselves, are of primary importance. The ancient Greeks were concerned with constructibility problems. For example, they tried to determine if it was possible, using straightedge and compass alone, to perform any of the following tasks? (1) Double an arbitrary cube; in particular, construct a cube with volume twice that of the unit cube. (2) Trisect an arbitrary angle. (3) Square an arbitrary circle; in particular, construct a square with area 1r. (4) Construct a regular polygon with n sides for n > 2. If we define a real number c to be constructible if, and only if, the point (c, 0) can be constructed starting with the points (0,0) and (1,0), then we may show that the set of constructible numbers is a subfield of the field R of real numbers containing the field Q of rational numbers. Such a subfield is called an intermediate field of Rover Q. We may thus gain insight into the constructibility problems by studying intermediate fields of Rover Q. In c
出版日期Textbook 1998Latest edition
關(guān)鍵詞Abelian group; Abstract Algebra; Division; Vector space; algebra; ksa
版次2
doihttps://doi.org/10.1007/978-1-4612-1792-3
isbn_softcover978-1-4612-7285-4
isbn_ebook978-1-4612-1792-3
copyrightSpringer Science+Business Media New York 1998
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,Preliminaries — Groups and Rings,eft as exercises, the majority of the proofs in the first two sections are presented fully as we guide the student through the process of studying groups via their normal subgroups and quotient groups.
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,Preliminaries — Groups and Rings,tary theory of groups and rings, concentrating on examples that will be used in later chapters. Although some of the more straightforward proofs are left as exercises, the majority of the proofs in the first two sections are presented fully as we guide the student through the process of studying gro
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978-1-4612-7285-4Springer Science+Business Media New York 1998
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The Galois Correspondence, extension of . and . has characteristic 0, then . = [.] and there is a one-to-one, order reversing correspondence between the set of intermediate fields of the extension . and the set of subgroups of . We will then show that this correspondence also preserves normality.
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