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Author: Jew-Chen John Hwang
Publisher:
ISBN:
Category : Equations, Cubic
Languages : en
Pages : 212
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Book Description
Author: Jew-Chen John Hwang
Publisher:
ISBN:
Category : Equations, Cubic
Languages : en
Pages : 212
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Book Description
Author: Jew-Chen (John). Hwang
Publisher:
ISBN:
Category : Equations, Cubic
Languages : fr
Pages : 106
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Book Description
Author: Ali Ovais
Publisher: LAP Lambert Academic Publishing
ISBN: 9783659260360
Category :
Languages : en
Pages : 60
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Book Description
There are many motivational problems related to the non-pure fields extension corresponding to the algebraic numbers (1+(r) DEGREES(1/n)) DEGREES(1/m), where m and n are positive integers. Here we take the extended field K over the field of rational numbers Q of degree n correspond to the inner nth root of the algebraic number and then the relative extension of degree m is taken over field K. If we interchange these nth and mth root then the whole structure and the resulting Hasse diagram change completely. In chapter 4 We have posed an open problem for the non-pure sextic field whose Galois closure is of extension degree 36. Since there are 14 groups of order 36 out of which four are abelian and ten are non-abelian and our group of automorphism is non-abelian so it is one of the ten. We had not only found this group but also create the correspondence between the Hasse diagram of subfields of Galois closure and the subgroups of group of aut
Author: Ka Lun Wong
Publisher:
ISBN:
Category :
Languages : en
Pages : 51
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Book Description
Maximal unramified extensions of quadratic number fields have been well studied. This thesis focuses on maximal unramified extensions of cyclic cubic fields. We use the unconditional discriminant bounds of Moreno to determine cyclic cubic fields having no non-solvable unramified extensions. We also use a theorem of Roquette, developed from the method of Golod-Shafarevich, and some results by Cohen to construct cyclic cubic fields in which the unramified extension is of infinite degree.
Author: M. Ishida
Publisher: Springer
ISBN: 3540375538
Category : Mathematics
Languages : en
Pages : 123
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Book Description
a
Author: Franz Halter-Koch
Publisher: CRC Press
ISBN: 0429014678
Category : Mathematics
Languages : en
Pages : 595
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Book Description
The author offers a thorough presentation of the classical theory of algebraic numbers and algebraic functions which both in its conception and in many details differs from the current literature on the subject. The basic features are: Field-theoretic preliminaries and a detailed presentation of Dedekind’s ideal theory including non-principal orders and various types of class groups; the classical theory of algebraic number fields with a focus on quadratic, cubic and cyclotomic fields; basics of the analytic theory including the prime ideal theorem, density results and the determination of the arithmetic by the class group; a thorough presentation of valuation theory including the theory of difference, discriminants, and higher ramification. The theory of function fields is based on the ideal and valuation theory developed before; it presents the Riemann-Roch theorem on the basis of Weil differentials and highlights in detail the connection with classical differentials. The theory of congruence zeta functions and a proof of the Hasse-Weil theorem represent the culminating point of the volume. The volume is accessible with a basic knowledge in algebra and elementary number theory. It empowers the reader to follow the advanced number-theoretic literature, and is a solid basis for the study of the forthcoming volume on the foundations and main results of class field theory. Key features: • A thorough presentation of the theory of Algebraic Numbers and Algebraic Functions on an ideal and valuation-theoretic basis. • Several of the topics both in the number field and in the function field case were not presented before in this context. • Despite presenting many advanced topics, the text is easily readable. Franz Halter-Koch is professor emeritus at the university of Graz. He is the author of “Ideal Systems” (Marcel Dekker,1998), “Quadratic Irrationals” (CRC, 2013), and a co-author of “Non-Unique Factorizations” (CRC 2006).
Author: Ivan B. Fesenko
Publisher: American Mathematical Society(RI)
ISBN:
Category : Mathematics
Languages : en
Pages : 312
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Book Description
Author: Tamara Lynn Smithee
Publisher:
ISBN:
Category : Algebraic fields
Languages : en
Pages : 68
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Book Description
Author: Kalyan Chakraborty
Publisher: Springer Nature
ISBN: 981151514X
Category : Mathematics
Languages : en
Pages : 182
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Book Description
This book gathers original research papers and survey articles presented at the “International Conference on Class Groups of Number Fields and Related Topics,” held at Harish-Chandra Research Institute, Allahabad, India, on September 4–7, 2017. It discusses the fundamental research problems that arise in the study of class groups of number fields and introduces new techniques and tools to study these problems. Topics in this book include class groups and class numbers of number fields, units, the Kummer–Vandiver conjecture, class number one problem, Diophantine equations, Thue equations, continued fractions, Euclidean number fields, heights, rational torsion points on elliptic curves, cyclotomic numbers, Jacobi sums, and Dedekind zeta values. This book is a valuable resource for undergraduate and graduate students of mathematics as well as researchers interested in class groups of number fields and their connections to other branches of mathematics. New researchers to the field will also benefit immensely from the diverse problems discussed. All the contributing authors are leading academicians, scientists, researchers, and scholars.
Author:
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 742
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Book Description
