Sökning: "Galois field"

Hittade 5 uppsatser innehållade orden Galois field.

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

    Kandidat-uppsats, Umeå universitet/Institutionen för matematik och matematisk statistik

    Författare :Axel Sjöblom; [2024]
    Nyckelord :;

    Sammanfattning : 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. LÄS MER

  3. 2. Profinite groups

    Master-uppsats, Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

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

    Sammanfattning : 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. LÄS MER

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

    Kandidat-uppsats, Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)

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

    Sammanfattning : 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. LÄS MER

  5. 4. An Exploration of Galois Theory with some Classical Results

    Kandidat-uppsats, Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematik LTH

    Författare :Olof Klingberg; [2020]
    Nyckelord :Galois theory; Algebra; Field theory; Mathematics and Statistics;

    Sammanfattning : Galois theory unites field theory and group theory to solve some field theoretical problems. The aim of this thesis is to provide a concise introduction to the topic, culminating in the proof of the insolubility of the general quintic equation by radicals. LÄS MER

  7. 5. Efficient Message Passing Decoding Using Vector-based Messages

    Uppsats för yrkesexamina på grundnivå, Institutionen för systemteknik

    Författare :Mikael Grimnell; Mats Tjäder; [2005]
    Nyckelord :Forward Error Correction; Low Density Parity Check Codes; Message Passing Decoding; Belief Propagation; Extrinsic Information Transfer; Galois Fields; Phase Shift Keying;

    Sammanfattning : The family of Low Density Parity Check (LDPC) codes is a strong candidate to be used as Forward Error Correction (FEC) in future communication systems due to its strong error correction capability. Most LDPC decoders use the Message Passing algorithm for decoding, which is an iterative algorithm that passes messages between its variable nodes and check nodes. LÄS MER