Global ETD Search

1	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. Field extensions (Mathematics) Abelian groups.
2	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])
3	Die Andersonextension und 1-motive Brinkmann, Christoph. January 1991 (has links) Thesis (Doctoral)--Universität Bonn, 1991. / Includes bibliographical references.
4	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.
5	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.
6	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).
7	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.
8	Explicit class field theory for rational function fields Rakotoniaina, Tahina 12 1900 (has links) Thesis (MSc (Mathematical Sciences))--Stellenbosch University, 2008. / Class field theory describes the abelian extensions of a given field K in terms of various class groups of K, and can be viewed as one of the great successes of 20th century number theory. However, the main results in class field theory are pure existence results, and do not give explicit constructions of these abelian extensions. Such explicit constructions are possible for a variety of special cases, such as for the field Q of rational numbers, or for quadratic imaginary fields. When K is a global function field, however, there is a completely explicit description of the abelian extensions of K, utilising the theory of sign-normalised Drinfeld modules of rank one. In this thesis we give detailed survey of explicit class field theory for rational function fields over finite fields, and of the fundamental results needed to master this topic. Class field theory Function fields Drinfeld modules Carlitz module Number theory Theses -- Mathematics Dissertations -- Mathematics Numbers, Rational Cyclotomic fields Function algebras Field extensions (Mathematics) Mathematical Sciences

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