In this dissertation, we consider six Prufer-like conditions on acommutative ring R. These conditions form a hierarchy. Being a Prufer ring is not a local property: a Prufer ring may not remain a Prufer ring when localized at a prime or maximal ideal. We introduce a seventh condition based on this fact and extend the hierarchy. All the conditions of the hierarchy become equivalent in the case of a domain, namely a Prufer domain. We also seek the relationship of the hierarchy with strong Prufer rings. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2015 / FAU Electronic Theses and Dissertations Collection

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Esta dissertaÃÃo està dividida em dois capÃtulos. O primeiro capÃtulo apresenta os AnÃis de Grupos, os Grupos de Frobenius e suas respectivas propriedades. No inÃcio do segundo capÃtulo sÃo apresentadas as Conjecturas de Zassenhaus. A versÃo mais fraca dessas conjecturas à demonstrada para Grupos de Amitsur. No final do segundo capÃtulo, a validade dessa mesma versÃo à provada para Grupos de Frobenius.Tais Grupos de Frobenius sÃo aqueles cujo complemento verifica-se a validade dessa conjectura. Na parte final sÃo apresentados os subgrupos de Hall e o Teorema de Schur-Zassenhaus. / This dissertation is divided into two chapters. The first chapter introduces the Group Rings, the Frobenius Groups and their properties. In the beginning of the second chapter are presented Conjectures of Zassenhaus . The weaker version of these conjectures is demonstrated for Amitsur Groups. At the end of the second chapter, the validity of that version is proven to Frobenius Groups. Such Frobenius Groups are those whose complement, checks the validity of this conjecture. In the final part we present the Hall subgroups and Schur-Zassenhaus Theorem.

Orientador: Renato Baldini Filho / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-26T06:28:30Z (GMT). No. of bitstreams: 1 Penze_ZelmannStrobe_D.pdf: 1452146 bytes, checksum: 44deab3ba8e13389a1bb2398482e35d5 (MD5) Previous issue date: 2014 / Resumo: Este trabalho apresenta uma proposta de simplificação do esquema de codificação turbo convencional com a utilização de um esquema de transmissão cooperativo. Os códigos turbos multiníveis convencionais consistem de dois códigos componentes M-ários, gerados a partir de dois codificadores sistemáticos recursivos, concatenados via um entrelaçador aleatório de N símbolos. No esquema proposto, apenas um codificador sistemático recursivo de taxa ½ é utilizado na fonte. A sequência de símbolos codificada é radiodifundida para o relay (retransmissor) e o destino. No relay esta sequência é detectada e decodificada utilizando um decodificador de Viterbi. Após a obtenção da sequência de informação transmitida pela fonte ao relay, esta informação depois de entrelaçada é novamente codificada por um codificador sistemático recursivo, idêntico ao da fonte. Contudo, apenas a porção da paridade gerada pelo codificador é enviada pelo relay ao destino. No destino, os dados recebidos da fonte e do relay são reordenados de forma que o decodificador considere que os dados foram transmitidos utilizando um esquema de codificação turbo multinível tradicional. Desta forma o esquema proposto utiliza das características peculiares dos códigos turbo definidos sobre anel de inteiros módulo-M em sistemas que utilizam a codificação cooperativa com o objetivo de obter ganhos de desempenho mesmo quando o canal direto encontra-se comprometido pelo desvanecimento. Além disso, avaliar esquemas de codificação que permitem a possibilidade de fracionar o processo de codificação no percurso cooperativo de modo a economizar banda no dispositivo retransmissor que colabora com a transmissão entre a fonte e o destino / Abstract: This work presents a proposal to simplify the conventional turbo coding scheme with the use of a cooperative transmission scheme. The conventional multilevel turbo codes consist of two M-ary RSC component codes concatenated via a random N-symbol interleaver. In the proposed scheme only one recursive systematic encoder with rate ½ is used. The sequence of coded symbols is broadcasted to the relay and the destination. At the relay, this sequence is detected and decoded using a Viterbi decoder. After obtaining the sequence information transmitted from the source to the relay, the information is again encoded by a recursive systematic encoder identical to the one in the source. However, only a portion of the parity generated by the encoder is sent from the relay to the destination. Data received at the destination from the source and the relay are reordered so that the decoder considers that the data were transmitted using a conventional multilevel turbo scheme. The aim of this work is to exploit some characteristics of turbo codes defined over ring of integers modulo-M in coded cooperation schemes. Moreover, it is intended to evaluate fractionary coding processes applied to the cooperative path in order to save band at the relay / Doutorado / Telecomunicações e Telemática / Doutor em Engenharia Elétrica

We study ideals of pointfree function rings. In particular, we study the lattices of z-ideals and d-ideals of the ring RL of continuous real-valued functions on a completely regular frame L. We show that the lattice of z-ideals is a coherently normal Yosida frame; and the lattice of d-ideals is a coherently normal frame. The lattice of z-ideals is demonstrated to be atly projectable if and only if the ring RL is feebly Baer. On the other hand, the frame of d-ideals is projectable precisely when the frame is cozero-complemented. These ideals give rise to two functors as follows: Sending a frame to the lattice of these ideals is a functorial assignment. We construct a natural transformation between the functors that arise from these assignments. We show that, for a certain collection of frame maps, the functor associated with z-ideals preserves and re ects the property of having a left adjoint. A ring is called a UMP-ring if every maximal ideal in it is the union of the minimal prime ideals it contains. In the penultimate chapter we give several characterisations for the ring RL to be a UMP-ring. We observe, in passing, that if a UMP ring is a Q-algebra, then each of its ideals when viewed as a ring in its own right is a UMP-ring. An example is provided to show that the converse fails. Finally, piggybacking on results in classical rings of continuous functions, we show that, exactly as in C(X), nth roots exist in RL. This is a consequence of an earlier proposition that every reduced f-ring with bounded inversion is the ring of fractions of its bounded part relative to those elements in the bounded part which are units in the bigger ring. We close with a result showing that the frame of open sets of the structure space of RL is isomorphic to L. / Mathematical Sciences / D.Phil. (Mathematics)

In his study of spectra of f-rings via pointfree topology, Banaschewski [6] considers lattices of l-ideals, radical l-ideals, and saturated l-ideals of a given f-ring A. In each case he shows that the lattice of each of these kinds of ideals is a coherent frame. This means that it is compact, generated by its compact elements, and the meet of any two compact elements is compact. This will form the basis of our main goal to show that the lattice-ordered rings studied in [6] are coherent frames. We conclude the dissertation by revisiting the d-elements of Mart nez and Zenk [30], and characterise them analogously to d-ideals in commutative rings. We extend these characterisa-tions to algebraic frames with FIP. Of necessity, this will require that we reappraise a great deal of Banaschewski's work on pointfree spectra, and that of Mart nez and Zenk on algebraic frames. / Mathematical Sciences / M. Sc. (Mathematics)

Orientador: Plamen Emilov Kochloukov / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-19T21:39:41Z (GMT). No. of bitstreams: 1 Mello_ThiagoCastilhode_D.pdf: 1364753 bytes, checksum: 66955ce4a4c6b84e5c6dcc1a414f3f24 (MD5) Previous issue date: 2012 / Resumo: Nesta tese estudamos a álgebra genérica de M1;1 em dois geradores sobre um corpo infinito de característica diferente de 2. Descrevemos o centro desta álgebra e provamos que este é a soma direta do corpo com um ideal nilpotente da álgebra. Como consequência mostramos que este centro contém elementos não escalares, respondendo a uma pergunta feita por Berele. Em característica zero, estudamos também as identidades polinomiais de tal álgebra genérica e exibimos uma base finita para seu T-ideal, utilizando a descrição do seu centro e os resultados de Popov sobre as identidades de M1;1 em característica zero. Segue que tal base é formada pelos polin^omios [x1; x2][x3; x4][x5; x6], [[x1; x2][x3; x4]; x5] e s4, a identidade polinomial standard de grau 4. Por fim, utilizando ideias e resultados de Nikolaev sobre as identidades em duas variáveis de M2(K) em característica zero, mostramos que todas as identidades polinomiais em duas variáveis de M1;1 são consequências das identidades [[x1; x2]2; x1] e [x1; x2]³ / Abstract: In this thesis, we study the generic algebra of M1;1 in two generators over an infinite field of characteristic different from 2. We describe the centre of this algebra and prove that this centre is a direct sum of the field and a nilpotent ideal of the algebra. As a consequence, we show that such centre contains nonscalar elements and thus we answer a question posed by Berele. In characteristic zero we also study the identities of this generic algebra and find a finite basis for its ideal of identities using the description of its centre and the results of Popov, about the identities of M1;1 in characteristic zero. It follows that such a basis is formed by the polynomials [x1; x2][x3; x4][x5; x6], [[x1; x2][x3; x4]; x5] and by s4, the standard identity of degree four. Finally, using ideas and results of Nikolaev about the identities in two variables of M2(K) in characteristic zero, we show that the polynomial identities in two variables of M1;1 follow from [[x1; x2]2; x1] and [x1; x2]³ / Doutorado / Matematica / Doutor em Matemática

Orientador: Reginaldo Palazzo Júnior / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-18T18:43:43Z (GMT). No. of bitstreams: 1 Faria_LuzineteCristinaBonanide_D.pdf: 17107444 bytes, checksum: 4faf2de7876247b3c74423dc7a3043d1 (MD5) Previous issue date: 2011 / Resumo: Um dos grandes desafios da comunidade científica em teorias da informação genética, comunicação genética e codificação genética é verificar a existência de uma estrutura matemática relacionada com a estrutura do DNA. Este trabalho propõe modelos para o sistema de comunicação de informação genética e genômica análogos ao modelo de um sistema de comunicação digital. Ambos os modelos são capazes de identificar, reproduzir e classificar matematicamente diferentes sequências de DNA. O primeiro identifica e reproduz a sequência de nucleotídeos de uma fita simples do DNA através da codificação genética e, o segundo identifica e reproduz a sequência das bases complementares da fita dupla do DNA através da codificação genômica. Os objetivos principais do presente trabalho são: a) caracterização matemática dos modelos de codificação genética e codificação genômica, b) proposta de um algoritmo para identificação de sequências de DNA; c) mostrar que sequências de DNA com características biológicas distintas, incluindo proteínas, gene e genoma em termos das fitas simples do DNA e da dupla hélice do DNA são identificadas como palavras-código dos códigos G-linearidade (BCH sobre corpos e BCH sobre anéis), reproduzidas e classificadas matematicamente, d) representação algébrica via polinômios primitivos/geradores e seus polinômios recíprocos das fitas simples do DNA (fita codante e fita não codante) e da dupla hélice do DNA, e) mostrar a existência de códigos concatenados (nested codes) entre algumas sequências de direcionamento e suas respectivas proteínas organelares, f) mostrar a arquitetura biológica (Biological frame) do genoma do plasmídeo Lactococcus lactis. Os resultados apresentados neste trabalho contribuem para o desenvolvimento de uma metodologia que poderá ser aplicada em análises mutacionais e de polimorfismos, produção de novos fármacos, melhoramento genético, entre outros, reduzindo tempo e custos laboratoriais / Abstract: One of the great challenges of the scientific community on theories of genetic information, genetic communication and genetic coding is to determine a mathematical structure related to the structure of DNA. This thesis proposes a model of a communication system for genetic and genomic information similar to the model of a digital communication system. Both models are able to identify, reproduce and classify mathematically different sequences of DNA. The first model identifies and reproduces the nucleotide sequence of a single DNA strand via the genetic encoding. The latter identifies and reproduces the sequence of the complementary bases of the double DNA strand through genomic encoding. The aims of this work are: a) a mathematical characterization of the models of genetic coding and genomic coding, b) the proposal of an algorithm for the identification of DNA sequences, c) to show that DNA sequences with distinct biological characteristics, including protein, gene and genome in terms of the single strands of DNA and of the double helix of DNA are identified as codewords of the G-linearity codes (BCH codes over fields and BCH codes over rings), mathematically reproduced and classified, d) algebraic representation via primitive/generator polynomials and their reciprocal polynomials of single DNA strands (coding strand and non-coding strand) and the double DNA strand, e) to show the existence of concatenated codes (nested codes) between some targeting sequences and their corresponding organelles proteins, f) to show the biological architecture (Biological frame) of the plasmid Lactococcus lactis genome. The results presented in this work contribute to the development of a methodology that can be applied to mutational analysis and polymorphisms, production of new drugs, genetic improvement, among others, reducing time and laboratory costs / Doutorado / Telecomunicações e Telemática / Doutor em Engenharia Elétrica

We study variants of P-frames and associated rings, which can be viewed as natural generalizations of the classical variants of P-spaces and associated rings. To be more precise, we de ne quasi m-rings to be those rings in which every prime d-ideal is either maximal or minimal. For a completely regular frame L, if the ring RL of real-valued continuous functions of L is a quasi m-ring, we say L is a quasi cozero complemented frame. These frames are less restricted than the cozero complemented frames. Using these frames we study some properties of what are called quasi m-spaces, and observe that the property of being a quasi m-space is inherited by cozero subspaces, dense z- embedded subspaces, and regular-closed subspaces among normal quasi m-space. M. Henriksen, J. Mart nez and R. G. Woods have de ned a Tychono space X to be a quasi P-space in case every prime z-ideal of C(X) is either minimal or maximal. We call a point I of L a quasi P-point if every prime z-ideal of RL contained in the maximal ideal associated with I is either maximal or minimal. If all points of L are quasi P-points, we say L is a quasi P-frame. This is a conservative de nition in the sense that X is a quasi P-space if and only if the frame OX is a quasi P-frame. We characterize these frames in terms of cozero elements, and, among cozero complemented frames, give a su cient condition for a frame to be a quasi P-frame. A Tychono space X is called a weak almost P-space if for every two zero-sets E and F of X with IntE IntF, there is a nowhere dense zero-set H of X such that E F [H. We present the pointfree version of weakly almost P-spaces. We de ne weakly regular rings by a condition characterizing the rings C(X) for weak almost P-spaces X. We show that a reduced f-ring is weakly regular if and only if every prime z-ideal in it which contains only zero-divisors is a d-ideal. We characterize the frames L for which the ring RL of real-valued continuous functions on L is weakly regular. We introduce the notions of boundary frames and boundary rings, and use them to give another ring-theoretic characterization of boundary spaces. We show that X is a boundary space if and only if C(X) is a boundary ring. A Tychono space whose Stone- Cech compacti cation is a nite union of closed subspaces each of which is an F-space is said to be nitely an F-space. Among normal spaces, S. Larson gave a characterization of these spaces in terms of properties of function rings C(X). By extending this notion to frames, we show that the normality restriction can actually be dropped, even in spaces, and thus we sharpen Larson's result. / Mathematics / D. Phil. (Mathematics)