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Relevant bibliographies by topics / Galois ring / Dissertations / Theses

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Dissertations / Theses on the topic 'Galois ring'

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Published: 4 June 2021

Last updated: 11 February 2022

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1

Hedenlund, Alice. "Galois Theory of Commutative Ring Spectra." Thesis, KTH, Matematik (Avd.), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-183512.

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This thesis discusses Galois theory of ring spectra in the sense of John Rognes. The aim is to give a clear introduction that provides a solid foundation for further studies into the subject. We introduce ring spectra using the symmetric spectra of Hovey, Shipley and Smith, and discuss the symmetric monoidal model structure on this category. We deﬁne and give results for Galois extensions of these objects. We also give examples involving Eilenberg-Mac Lane spectra of commutative rings, topological K-theory spectra and cochain algebras of these. Galois extensions of ring spectra are compared to

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2

Abrahamsson, Björn. "Architectures for Multiplication in Galois Rings." Thesis, Linköping University, Department of Electrical Engineering, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-2396.

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<p>This thesis investigates architectures for multiplying elements in Galois rings of the size 4^m, where m is an integer. </p><p>The main question is whether known architectures for multiplying in Galois fields can be used for Galois rings also, with small modifications, and the answer to that question is that they can. </p><p>Different representations for elements in Galois rings are also explored, and the performance of multipliers for the different representations is investigated.</p>

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3

Armand, Marc Andre. "Contributions to the decoding of linear codes over a Galois ring." Thesis, University of Bristol, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.297851.

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4

Moon, Yong Suk. "Galois Deformation Ring and Barsotti-Tate Representations in the Relative Case." Thesis, Harvard University, 2016. http://nrs.harvard.edu/urn-3:HUL.InstRepos:33493581.

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In this thesis, we study finite locally free group schemes, Galois deformation rings, and Barsotti-Tate representations in the relative case. We show three independent but related results, assuming p > 2. First, we give a simpler alternative proof of Breuil’s result on classifying finite flat group schemes over the ring of integers of a p-adic field by certain Breuil modules [5]. Second, we prove that the locus of potentially semi-stable representations of the absolute Galois group of a p-adic field K with a specified Hodge-Tate type and Galois type cuts out a closed subspace of the generic f

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5

Szabo, Steve. "Convolutional Codes with Additional Structure and Block Codes over Galois Rings." Ohio University / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1257792383.

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6

Pinnawala, Nimalsiri, and nimalsiri pinnawala@rmit edu au. "Properties of Trace Maps and their Applications to Coding Theory." RMIT University. Mathematical and Geospatial Sciences, 2008. http://adt.lib.rmit.edu.au/adt/public/adt-VIT20080515.121603.

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In this thesis we study the application of trace maps over Galois fields and Galois rings in the construction of non-binary linear and non-linear codes and mutually unbiased bases. Properties of the trace map over the Galois fields and Galois rings has been used very successfully in the construction of cocyclic Hadamard, complex Hadamard and Butson Hadamard matrices and consequently to construct linear codes over integers modulo prime and prime powers. These results provide motivation to extend this work to construct codes over integers modulo . The prime factorization of integers paved

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7

Herschend, Martin. "On the Clebsch-Gordan problem for quiver representations." Doctoral thesis, Uppsala University, Department of Mathematics, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-8663.

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<p>On the category of representations of a given quiver we define a tensor product point-wise and arrow-wise. The corresponding Clebsch-Gordan problem of how the tensor product of indecomposable representations decomposes into a direct sum of indecomposable representations is the topic of this thesis.</p><p>The choice of tensor product is motivated by an investigation of possible ways to modify the classical tensor product from group representation theory to the case of quiver representations. It turns out that all of them yield tensor products which essentially are the same as the point-wise

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8

Lodh, Rémi Shankar. "Galois cohomology of Fontaine rings." [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=984696563.

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9

Turner, Ryan. "The Galois theory of matrix C-rings." Thesis, Swansea University, 2006. https://cronfa.swan.ac.uk/Record/cronfa42607.

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10

Blackford, J. Thomas. "Permutation groups of extended cyclic codes over Galois Rings /." The Ohio State University, 1999. http://rave.ohiolink.edu/etdc/view?acc_num=osu1488186329502909.

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11

Raji, Mehrdad Ahmadzadeh. "High power residue codes over Galois rings and related lattices." Thesis, University of Exeter, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.248091.

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12

Villafranca, Rogério. "Decodificação de códigos sobre anéis de Galois." reponame:Repositório Institucional da UFABC, 2014.

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Orientador: Prof. Dr. Francisco César Polcino Milies<br>Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Matemática , 2014.<br>Códigos sobre anéis vem sendo estudados desde a década de 70 e hoje sabe-se que alguns códigos não-lineares sobre corpos são imagens de códigos lineares sobre anéis Zpm. Neste trabalho, lidamos com códigos sobre Anéis de Galois, que são uma generalização tanto para corpos finitos quanto para anéis Zpm. Em uma primeira parte dedicada a anéis, definimos anéis de Galois como um caso particular de anéis locais, mostramos a equivalência ent

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13

Katz, Daniel J. Wilson R. M. "On p-adic estimates of weights in Abelian codes over Galois rings /." Diss., Pasadena, Calif. : California Institute of Technology, 2005. http://resolver.caltech.edu/CaltechETD:etd-05312005-175744.

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14

Guiraud, David-Alexandre [Verfasser], and Gebhard [Akademischer Betreuer] Böckle. "A framework for unobstructedness of Galois deformation rings / David-Alexandre Guiraud ; Betreuer: Gebhard Böckle." Heidelberg : Universitätsbibliothek Heidelberg, 2016. http://d-nb.info/1180610385/34.

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15

Rzedowski-Calderon, Martha. "Galois module structure of rings of integers and automorphism groups of congruence function fields /." The Ohio State University, 1988. http://rave.ohiolink.edu/etdc/view?acc_num=osu148759571215722.

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16

Park, Chol. "Semi-Stable Deformation Rings in Hodge-Tate Weights (0,1,2)." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/293444.

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In this dissertation, we study semi-stable representations of G(Q(p)) and their mod p-reductions, which is a part of the problem in which we construct deformation spaces whose characteristic 0 closed points are the semi-stable lifts with Hodge-Tate weights (0, 1, 2) of a fixed absolutely irreducible residual representation ρ : G(Q(p)) → GL₃(F(p)). We first classify the isomorphism classes of semi-stable representations of G(Q(p)) with regular Hodge-Tate weights, by classifying admissible filtered (phi,N)-modules with Hodge-Tate weights (0, r, s) for 0 < r < s. We also construct a Galois stable

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17

Khalil, Maya. "Classes de Steinitz, codes cycliques de Hamming et classes galoisiennes réalisables d'extensions non abéliennes de degré p³." Thesis, Valenciennes, 2016. http://www.theses.fr/2016VALE0012/document.

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18

Sampaio, Ingrid Araujo. "Codigos ciclicos sobre aneis locais e suas relações com a transformada discreta de Fourier." [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/259782.

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Orientador: Reginaldo Palazzo Junior<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação<br>Made available in DSpace on 2018-08-09T21:06:53Z (GMT). No. of bitstreams: 1 Sampaio_IngridAraujo_M.pdf: 836393 bytes, checksum: c88f5bde14a891b8579e6d9dca463a95 (MD5) Previous issue date: 2007<br>Resumo: Neste trabalho apresentamos algumas relações existentes entre codigos c'clicos e a transformada discreta de Fourier ambos sobre aneis locais. Para isso, 'e necessario a identificação do grupo das unidades associado a cada um dos anéis consid

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19

Dario, Ronie Peterson. "Propriedades aritmeticas de corpos com um anel de valorização compativel com o radical de Kaplansky." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306508.

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Orientador: Antonio Jose Engler<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-10T18:05:59Z (GMT). No. of bitstreams: 1 Dario_RoniePeterson_D.pdf: 1951766 bytes, checksum: afa64043636e06c86924e24d6fe65f43 (MD5) Previous issue date: 2008<br>Resumo: Esta tese é um estudo das propriedades aritméticas de corpos que possuem um anel de valorização compatível com o Radical de Kaplansky. São utilizados os métodos da teoria algébrica das formas quadráticas, teoria de Galois e principalmente,

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20

Ferreira, Mauricio de Araujo 1982. "Algebras biquaternionicas : construção, classificação e condições de existencia via formas quadraticas e involuções." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306541.

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Orientador: Antonio Jose Engler<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-05T18:56:31Z (GMT). No. of bitstreams: 1 Ferreira_MauriciodeAraujo_M.pdf: 1033477 bytes, checksum: 8d697b5cdeb1a633c1270a5e2f919de7 (MD5) Previous issue date: 2006<br>Resumo: Neste trabalho, estudamos as álgebras biquaterniônicas, que são um tipo especial de álgebra central simples de dimensão 16, obtida como produto tensorial de duas álgebras de quatérnios. A teoria de formas quadráticas é aplicada

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21

Santos, Duilio Ferreira. "Elementos da teoria algébrica das formas quadráticas e de seus anéis graduados." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-22062016-104927/.

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Neste trabalho procuramos realizar uma apresentação autocontida sobre os conceitos da teoria algébrica de formas quadráticas e sobre os anéis graduados que surgiram no desenvolvimento desta teoria. Iniciamos procurando esclarecer o sentido da equivalência entre as várias acepções do conceito de forma quadrática. Após a apresentação de ingredientes e resultados geométricos, fazemos um extrato da teoria dos anéis de Witt, conceito que originou a moderna teoria algébrica de formas quadráticas. Disponibilizamos os elementos fundamentais para a formulação das teorias de cohomologia, nos concentrado

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22

Izquierdo, Diego. "Dualité et principe local-global sur les corps de fonctions." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLS345/document.

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Dans cette thèse, nous nous intéressons à l'arithmétique de certains corps de fonctions. Nous cherchons à établir dans un premier temps des théorèmes de dualité arithmétique sur ces corps, pour les appliquer ensuite à l'étude des points rationnels sur certaines variétés algébriques. Dans les trois premiers chapitres, nous travaillons sur le corps des fonctions d'une courbe sur un corps local supérieur (comme Qp, Qp((t)), C((t)) ou C((t))((u))). Dans le premier chapitre, nous établissons sur un tel corps des théorèmes de dualité arithmétique « à la Poitou-Tate » pour les modules finis, les tore

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23

Wu, ping-ta, and 吳秉達. "The structure of Galois rings and the structure of finite local rings." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/21978780360538928711.

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碩士<br>國立中正大學<br>數學系研究所<br>105<br>We want to study the structure of Galois rings and analyze the unit of the Galois rings. And we will show that each finite commutative ring can be considered as a suitable algebra over a fixed Galois ring.

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24

Lodh, Rémi Shankar [Verfasser]. "Galois cohomology of Fontaine rings / vorgelegt von Rémi Shankar Lodh." 2007. http://d-nb.info/984696563/34.

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25

Katz, Daniel Jerome. "On p-Adic Estimates of Weights in Abelian Codes over Galois Rings." Thesis, 2005. https://thesis.library.caltech.edu/2329/1/djkatz_thesis.pdf.

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<p>Let p be a prime. We prove various analogues and generalizations of McEliece's theorem on the p-divisibility of weights of words in cyclic codes over a finite field of characteristic p. Here we consider Abelian codes over various Galois rings. We present four new theorems on p-adic valuations of weights. For simplicity of presentation here, we assume that our codes do not contain constant words.</p> <p>The first result has two parts, both concerning Abelian codes over Z/p<sup>d</sup>Z. The first part gives a lower bound on the p-adic valuations of Hamming weights. This bound is sho

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26

Procházková, Zuzana. "Význačné prvky grupových okruhů." Master's thesis, 2021. http://www.nusl.cz/ntk/nusl-448402.

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Title: Distinguished elements of group rings Author: Bc. Zuzana Procházková Department: Department of Algebra Supervisor: doc. Mgr. et Mgr. Jan Žemlička, Ph.D., Department of Algebra Abstract: This thesis is about finding idempotents in a group ring. We describe three techniques of finding idempotents in a semisimple group ring and in the last chapter there is an attempt to find idempotents in a group ring that does not have to be semisimple. The first technique uses representations and characters of a group. The second technique finds idempotents through the use of Shoda pairs. The third tech

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27

Hammond, John Lockwood. "Regular realizations of p-groups." 2008. http://hdl.handle.net/2152/18100.

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This thesis is concerned with the Regular Inverse Galois Problem for p-groups over fields of characteristic unequal to p. Building upon results of Saltman, Dentzer characterized a class of finite groups that are automatically realized over every field, and proceeded to show that every group of order dividing p⁴ belongs to this class. We extend this result to include groups of order p⁵, provided that the base field k contains the p³-th roots of unity. The proof involves reducing to certain Brauer embedding problems defined over the rational function field k(x). Through explicit computation, we

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