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On radical extensions and radical towers.Barrera Mora, Jose Felix Fernando. January 1989 (has links)
Let K/F be a separable extension. (i) If K = F(α) with αⁿ ∈ F for some n, K/F is said to be a radical extension. (ii) If there exists a sequence of fields F = F₀ ⊆ F₁ ⊆ ... ⊆ F(s) = K so that Fᵢ₊₁ = Fᵢ(αᵢ) with αᵢⁿ⁽ⁱ⁾ ∈ Fᵢ for some nᵢ ∈ N, charF ∧nᵢ for every i, and [Fᵢ₊₁ : Fᵢ] = nᵢ, K/F is said to be a radical tower. In the first part of this work, we present two theorems which give sufficient conditions for a field extension K/F to be radical. In the second part, we present results which provide conditions under which every subfield of a radical tower is also a radical tower.
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Topics in J-fields and a diameter problem /McAuley, Michael J. January 1981 (has links) (PDF)
Thesis (M.Sc.) -- Dept. of Pure Mathematics, University of Adelaide1983. / Typescript (photocopy).
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An examination of class number for [reproduction of quadratic extensions] where [reproduction of square root of d] has continued fraction expansion of period three /Young, Brent O. J. January 2005 (has links) (PDF)
Thesis (M.S.)--University of North Carolina at Wilmington, 2005. / Includes bibliographical references (Leaf: [104])
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Die Andersonextension und 1-motiveBrinkmann, Christoph. January 1991 (has links)
Thesis (Doctoral)--Universität Bonn, 1991. / Includes bibliographical references.
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Hopf-Galois structures on Galois extensions of fields of squarefree degreeAlabdali, Ali Abdulqader Bilal January 2018 (has links)
Hopf-Galois extensions were introduced by Chase and Sweedler [CS69] in 1969, motivated by the problem of formulating an analogue of Galois theory for inseparable extensions. Their approach shed a new light on separable extensions. Later in 1987, the concept of Hopf-Galois theory was further developed by Greither and Pareigis [GP87]. So, as a problem in the theory of groups, they explained the problem of finding all Hopf-Galois structures on a finite separable extension of fields. After that, many results on Hopf-Galois structures were obtained by N. Byott, T. Crespo, S. Carnahan, L. Childs, and T. Kohl. In this thesis, we consider Hopf-Galois structures on Galois extensions of squarefree degree n. We first determine the number of isomorphism classes of groups G of order n whose centre and commutator subgroup have given orders, and we describe Aut(G) for each such G. By investigating regular cyclic subgroups in Hol(G), we enumerate the Hopf-Galois structures of type G on a cyclic extension of fields L/K of degree n. We then determine the total number of Hopf-Galois structures on L/K. Finally, we examine Hopf-Galois structures on a Galois extension L/K with arbitrary Galois group Gamma of order n, and give a formula for the number of Hopf-Galois structures on L/K of a given type G.
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Generic Galois extensions for groups or order p³ /Blue, Meredith Patricia, January 2000 (has links)
Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 112-116). Available also in a digital version from Dissertation Abstracts.
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Trace forms and self-dual normal bases in Galois field extensions /Kang, Dong Seung. January 1900 (has links)
Thesis (Ph. D.)--Oregon State University, 2003. / Typescript (photocopy). Includes bibliographical references (leaves 43-46). Also available on the World Wide Web.
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The nonexistence of certain free pro-p extensions and capitulation in a family of dihedral extensions of Q /Hubbard, David, January 1996 (has links)
Thesis (Ph. D.)--University of Washington, 1996. / Vita. Includes bibliographical references (leaves [47]-48).
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Class groups of ZZ-extensions and solvable automorphism groups of algebraic function fields /D'Mello, Joseph Gerard January 1982 (has links)
No description available.
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Explicit class field theory for rational function fields /Rakotoniaina, Tahina. January 2008 (has links)
Thesis (MSc)--University of Stellenbosch, 2008. / Bibliography. Also available via the Internet.
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