Dissertations / Theses on the topic 'Galois ring'
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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.
Full textDenna uppsats behandlar Galoisutvidgningar av ringspektra som först introducerade av Rognes. Målet är att ge en klar introduktion för en sta-bil grund för vidare studier inom ämnet. Vi introducerar ringspektra genom att använda oss av symmetris-ka spektra utvecklade av Hovey, Shipley och Smith, och diskuterar den symmetriskt monoidiala modelstrukturen på denna kategori. Vi definierar och ger resultat för Galoisutvidgningar av dessa objekt. Vi ger också en mängd exempel, som till exempel utvidgningar av Eilenberg-Mac Lane spektra av kommutativa ringar, topologiska K-teorispektra och koked-jealgebror. Galoisutvidgningar av ringspektra jämförs med Galoisutvidgningar av kommutativa ringar, speciellt med avseende pa˚ trogenhet, en egenskap som ¨ar en inneboende egenskap hos den senare men inte i den förra. Detta visas genom att betrakta utvidgningar av kokedjealgebror av Eilenberg-Mac Lane spektra. Vi avslutar med att jämföra detta med kokedjealgebrautvidgningar av K-teorispektra och visar att sådana inte är Galois genom att använda metoder utvecklade av Baker och Richter
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.
Full textThis thesis investigates architectures for multiplying elements in Galois rings of the size 4^m, where m is an integer.
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.
Different representations for elements in Galois rings are also explored, and the performance of multipliers for the different representations is investigated.
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.
Full textMoon, 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.
Full textMathematics
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.
Full textPinnawala, 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.
Full textHerschend, 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.
Full textOn 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.
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 tensor product.
We solve the Clebsch-Gordan problem for all Dynkin quivers of type A, D and E6, and provide explicit descriptions of their respective representation rings. Furthermore, we investigate how the tensor product interacts with Galois coverings. The results obtained are used to solve the Clebsch-Gordan problem for all extended Dynkin quivers of type Ãn and the double loop quiver with relations βα=αβ=αn=βn=0.
Lodh, Rémi Shankar. "Galois cohomology of Fontaine rings." [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=984696563.
Full textTurner, Ryan. "The Galois theory of matrix C-rings." Thesis, Swansea University, 2006. https://cronfa.swan.ac.uk/Record/cronfa42607.
Full textBlackford, 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.
Full textRaji, 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.
Full textVillafranca, Rogério. "Decodificação de códigos sobre anéis de Galois." reponame:Repositório Institucional da UFABC, 2014.
Find full textDissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Matemática , 2014.
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 entre essa definição e a construção clássica desses anéis como extensões de Zpm e apresentamos propriedades importantes. Em seguida, na parte referente à Teoria de Códigos, descrevemos as bases necessárias desse assunto e apresentamos um método permitindo a obtenção de um algoritmo de decodificação para um código sobre um anel de Galois a partir de algoritmos de decodificação para códigos lineares sobre o corpo de resíduos desse anel.
Codes over rings are a research subject since the 70¿s and today is well known that some non-linear codes over fields are images of linear codes over Zpm rings. In this work we deal with codes over Galois rings, which generalize both finite fields and Zpm rings. In a first part concerning ring theory, we define Galois rings as a particular case of local rings, show the equivalence of this definition to the classical construction of such rings as extensions of Zpm and present important properties of these structures. Next, concerning Coding Theory, we describe the basic facts of this subject and present a method that alows us to obtain decoding alogrithms for a linear code over a Galois ring from decoding algorithms for linear codes over the residue field of that ring.
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.
Full textGuiraud, 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.
Full textRzedowski-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.
Full textPark, Chol. "Semi-Stable Deformation Rings in Hodge-Tate Weights (0,1,2)." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/293444.
Full textKhalil, 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.
Full textSampaio, 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.
Full textDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
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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 considerados. Como consequencia, codigos ciclicos sobre tais aneis podem ser construidos. Em seguida, construimos geradores de sequencias atravees dos registros de deslocamento com realimentação linear (LFSR), a partir dos polinomios geradores, cujos coeficientes pertencem a um corpo finito e a um anel comutativo finito local com identidade. Finalmente, realizamos a transformada discreta de Fourier por meio do polinomio gerador dos codigos ciclicos sobre aneis locais
Abstract: In this research we present some existing relationships between cyclic codes and discrete Fourier transform both local rings. For this, it is necessary to identify the groups of unit associated with each corresponding local ring. As a consequence, cyclic codes over these rings may be constructed. Next, we construct sequence generators by use of linear feedback shift register (LFSR), from generator polynomials whose coefficients belong either to finite field or to a local finite commutative ring with identity. Finally, the discrete Fourier transform is realized by use of the generator polynomial of cyclic codes over local rings
Mestrado
Telecomunicações e Telemática
Mestre em Engenharia Elétrica
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.
Full textTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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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, a teoria de valorizações em corpos. Apresentamos um novo método para a construção de corpos com Radical de Kaplansky não trivial. Demonstramos uma versão do Teorema 90 de Hilbert para o radical. Para uma álgebra quaterniônica D, demonstramos que um anel de valorização do centro de D possui extensão para um anel de valorização total e invariante de D se, e somente se, for compatível com o Radical de Kaplansky
Abstract: This thesis is a study of the arithmetical properties of fields with a valuation ring compatible with the Kaplansky¿s Radical. The methods utilized are algebraic theory of quadratic forms, Galois theory and valuation theory over fields. We present a new construction method of fields with non-trivial Kaplansky¿s Radical. We also prove a version of the Hilbert¿s 90 Theorem for the radical. Let D a quaternion algebra and F the center of D. A valuation ring of F has a extension to a total and invariant valuation ring of D iff is compatible with the Kaplansky¿s Radical
Doutorado
Algebra
Doutor em Matemática
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.
Full textDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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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 para estudarmos critérios de decisão sobre quando uma álgebra biquaterniônica é de divisão e quando duas destas álgebras são isomorfas. Além disso, utilizamos o u-invariante do corpo para discutirmos a existência de álgebras biquaterniônicas de divisão sobre o corpo. Provamos também um resultado atribuído a A. A. Albert, que estabelece critérios para decidir quando uma álgebra central simples de dimensão 16 é de fato uma álgebra biquaterniônica, através do estudo de involuções. Ao longo do trabalho, construímos vários exemplos concretos de álgebras biquaterniônicas satisfazendo propriedades importantes
Mestrado
Algebra
Mestre em Matemática
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/.
Full textIn this work I try to provide a self-contained presentation on the concepts of algebraic theory of quadratic forms and on the graded rings that have emerged in the development of this theory. I started trying to clarify the meaning of \"equivalence\"between the various meanings of the concept of quadratic form. After the presentation of geometrical ingredients and results, we make an extract of the theory of Witt rings, a concept that originated the modern algebraic theory of quadratic forms. It is provided the key elements for the formulation of cohomology theories, focusing on the development of profinite cohomology theory and, especially, on galoisian cohomology. Are described the functors K0, K1 and K2 of classical K-theory and also the Milnor K-theory, which is more appropriate to formulate questions about quadratic forms. The dissertation is finished with the presentation of some concepts of the Theory of Special Groups, a first-order encoding of algebraic theory of quadratic forms, and with an example its importance by providing an extract of proof by Dickmann-Miraglia of the Marshalls conjecture on signatures, which relies heavily on this theory.
Izquierdo, Diego. "Dualité et principe local-global sur les corps de fonctions." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLS345/document.
Full textIn this thesis, we are interested in the arithmetic of some function fields. We first want to establish arithmetic duality theorems over those fields, in order to apply them afterwards to the study of rational points on algebraic varieties. In the first three chapters, we work on the function field of a curve defined over a higher-dimensional local field (such as Qp, Qp((t)), C((t)) or C((t))((u))). In the first chapter, we establish "Poitou-Tate type" arithmetic duality theorems over such fields for finite modules, tori and even some complexes of tori. We also prove the existence, under some hypothesis, of parts of the corresponding Poitou-Tate exact sequences. These results are applied in the second chapter to the study of the local-global principle for central simple algebras, of weak approximation for tori, and of obstructions to local-global principle for torsors under connected linear algebraic groups. In the third chapter, we are interested in abelian varieties and we establish "Cassels-Tate type" arithmetic duality theorems. To do so, we also need to carry out a precise study of abelian varieties over higher-dimensional local fields. In the fourth and last chapter, we work on the field of fractions of some 2-dimensional normal local algebras (such as C((x, y)) or Fp((x, y))). We first establish in this context an "Artin-Verdier type" duality theorem in étale cohomology. This allows us to prove "Poitou-Tate type" arithmetic duality theorems in Galois cohomology for finite modules and tori. In the end, we apply these results to the study of weak approximation for tori and of obstructions to local-global principle for torsors under connected linear algebraic groups
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.
Full text國立中正大學
數學系研究所
105
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.
Lodh, Rémi Shankar [Verfasser]. "Galois cohomology of Fontaine rings / vorgelegt von Rémi Shankar Lodh." 2007. http://d-nb.info/984696563/34.
Full textKatz, 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.
Full textLet 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.
The first result has two parts, both concerning Abelian codes over Z/pdZ. The first part gives a lower bound on the p-adic valuations of Hamming weights. This bound is shown to be sharp: for each code, we find the maximum k such that pk divides all Hamming weights. The second part of our result concerns the number of occurrences of a given nonzero symbol s ∈ Z/pdZ in words of our code; we call this number the s-count. We find a j such that pj divides the s-counts of all words in the code. Both our bounds are stronger than previous ones for infinitely many codes.
The second result concerns Abelian codes over Z/4Z. We give a sharp lower bound on the 2-adic valuations of Lee weights. It improves previous bounds for infinitely many codes.
The third result concerns Abelian codes over arbitrary Galois rings. We give a lower bound on the p-adic valuations of Hamming weights. When we specialize this result to finite fields, we recover the theorem of Delsarte and McEliece on the p-divisibility of weights in Abelian codes over finite fields.
The fourth result generalizes the Delsarte-McEliece theorem. We consider the number of components in which a collection c_1,...,c_t of words all have the zero symbol; we call this the simultaneous zero count. Our generalized theorem p-adically estimates simultaneous zero counts in Abelian codes over finite fields, and we can use it to prove the theorem of N. M. Katz on the p-divisibility of the cardinalities of affine algebraic sets over finite fields.
Procházková, Zuzana. "Význačné prvky grupových okruhů." Master's thesis, 2021. http://www.nusl.cz/ntk/nusl-448402.
Full textHammond, John Lockwood. "Regular realizations of p-groups." 2008. http://hdl.handle.net/2152/18100.
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