Essays about: "Galois Theory"

Showing result 1 - 5 of 12 essays containing the words Galois Theory.

  1. 1. The Abel-Ruffini Theorem : The insolvability of the general quintic equation by radicals

    University essay from Umeå universitet/Institutionen för matematik och matematisk statistik

    Author : Axel Sjöblom; [2024]
    Keywords : ;

    Abstract : This thesis explores the topic of Galois theory at a relatively introductory level with the goal of proving the Abel Ruffini theorem. In the first part algebraic structures are considered: groups, ring, fields, etc. Following this, polynomial rings are introduced and the attention is then turned to finite field-extensions. READ MORE

  3. 2. The low-lying zeros of L-functions associated to non-Galois cubic fields

    University essay from Göteborgs universitet/Institutionen för matematiska vetenskaper

    Author : Victor Ahlquist; [2023-02-13]
    Keywords : Mathematics; number theory; cubic fields; L-functions; low-lying zeros; onelevel density; two-level density; phase transition.;

    Abstract : We study the low-lying zeros of Artin L-functions associated to non-Galois cubic number fields through their one- and two-level densities. In particular, we find new precise estimates for the two-level density with a power-saving error term. READ MORE

  4. 3. Profinite groups

    University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

    Author : Juan Moreno Poncela; [2023]
    Keywords : Profinite Groups; Infinite Galois Theory; Mathematics and Statistics;

    Abstract : This thesis provides a comprehensive study of profinite groups, which are fascinating mathematical objects that have attracted significant interest in modern algebraic research. Profinite groups are infinite generalizations of finite groups and share many similarities with them. READ MORE

  5. 4. An almost algebraic proof of the fundamental theorem of algebra

    University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)

    Author : David Kamali; [2021]
    Keywords : algebrans fundamentalsats; Sylows satser; kroppteori; Galoisteori; fundamental theorem of algebra; group theory; Sylow theorems; Galois Theory; field theory; Mathematics and Statistics;

    Abstract : By the results of the Sylow theorems, algebraic extension theorems and Galois theory, we shall prove the fundamental theorem of algebra, which states that the set of complex numbers is algebraically closed. This process of abstraction will provide an almost algebraic proof of the theorem and thereby supply us with a tool in solving many questions within the field of mathematics. READ MORE

  6. 5. Galois Theory and the Artin-Schreier Theorem

    University essay from Uppsala universitet/Algebra och geometri

    Author : Ebba Mellquist; [2020]
    Keywords : ;

    Abstract : .... READ MORE