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Dissertations / Theses on the topic 'Associative rings'
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Badawi, Ayman R. "π-regular Rings." Thesis, University of North Texas, 1993. https://digital.library.unt.edu/ark:/67531/metadc279388/.
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Montgomery, Martin. "Dimension of certain cleft binomial rings /." view abstract or download file of text, 2006. http://proquest.umi.com/pqdweb?did=1188874501&sid=7&Fmt=2&clientId=11238&RQT=309&VName=PQD.
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Thesis (Ph. D.)--University of Oregon, 2006.Typescript. Includes vita and abstract. Includes bibliographical references (leaf 77). Also available for download via the World Wide Web; free to University of Oregon users.
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Kriel, Marelize. "Endomorphism rings of hyperelliptic Jacobians." Thesis, Link to the online version, 2005. http://hdl.handle.net/10019/1077.
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Rivera, Roberto Rafael. "On properties of completely flexible loops." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/28841.
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Li, Yunchang, and 李云昌. "Degree estimate and preserving problems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/206360.
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Green, Ellen Yvonne. "Characterizing the strong two-generators of certain Noetherian domains." CSUSB ScholarWorks, 1997. https://scholarworks.lib.csusb.edu/etd-project/1539.
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Chin, Melanie Soo, and m. chin@cqu edu au. "Towards a Reinterpretation of the Radical Theory of Associative Rings Using Base Radical and Base Semisimple Class Constructions." Central Queensland University. Computer Science, 2004. http://library-resources.cqu.edu.au./thesis/adt-QCQU/public/adt-QCQU20050411.102928.
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This research aims to refresh and reinterpret the radical theory of associative rings using the base radical and base semisimple class constructions. It also endeavours to generalise some results about ideals of rings in terms of accessible subrings. A characterisation of accessible subrings is included. By applying the base radical and base semisimple class constructions to many of the known results in established radical theory a number of gaps are uncovered and closed, with the goal of making the theory more accessible to advanced undergraduate and graduate students and mathematicians in related fields, and to open up new areas of investigation.
After a literature review and brief reminder of algebra rudiments, the useful properties of accessible subrings and the U and S operators independent from radical class connections are described. The section on accessible subrings illustrates that replacing ideals with accessible subrings is indeed possible for a number of results and demonstrates its usefulness.
The traditional radical and semisimple class definitions are included and it is shown that the base radical and base semisimple class constructions are equivalent. Diagrams illustrating the constructions support the definitions. From then on, all radical and semisimple classes mentioned are understood to have the base radical and base semisimple class form. Subject to the constraints of this work, many known results of traditional radical theory are reinterpreted with new proofs, illustrating the potential to simplify the understanding of radical theory using the base radical and base semisimple class constructions. Along with reinterpreting known results, new results emerge giving further insight to radical theory and its intricacies. Accessible subrings and the U and S operators are integrated into the development. The duality between the base radical and base semisimple class constructions is demonstrated in earnest.
With a measure of the theory presented, the new constructions are applied to examples and concrete radicals. Context is supported by establishing the relationship between some well-known rings and the radical and related classes of interest.
The title of the thesis, Towards a Reinterpretation of the Radical Theory of Associative Rings Using Base Radical and Base Semisimple Class Constructions, reflects the understanding that reinterpreting the entirety of radical theory is beyond the scope of this work. The conclusion includes an outlook listing further research that time did not allow.
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Ferreira, Mauricio de Araujo 1982. "Funções valorização e anéis de valorização de Dubrovin em álgebras simples." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306563.
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Orientadores: Antonio José Engler, Adrian Roscoe WadsworthTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
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Resumo: Nesta tese estudamos a relação entre duas teorias de valorização não-comutativas: anéis de valorização de Dubrovin e gauges. Os anéis de valorização de Dubrovin foram introduzidos em 1982, como uma generalização para anéis artinianos simples dos anéis de valorização invariantes em álgebras de divisão. Gauges são funções como valorizações, que podem ser definidas não só em álgebra de divisão, mas mais geralmente em álgebras simples e até mesmo semi-simples, de dimensão finita sobre corpos valorizados. Gauges foram introduzidas muito mais recentemente em 2010 por Tignol e Wadsworth. Assim como em valorizações de corpos, podemos definir um anel associado a uma gauge, que chamamos de anel da gauge. Propriedades aritméticas do anel da gauge são estudadas. Mostramos que o anel de uma gauge é sempre uma ordem semi-local integral sobre seu centro. Também descrevemos o anel da gauge com relação a composição de gauges e extensão de escalares. Introduzimos o conceito de gauge minimal em álgebras centrais simples, que são gauges cuja parte de grau zero da álgebra graduada associada tem o menor número possível de componentes simples. Mostramos que o anel de uma gauge minimal coincide com a interseção de uma família de anéis de valorização de Dubrovin, satisfazendo uma propriedade adicional, que foi introduzida por Gräter em 1992, e que é chamada de propriedade da interseção. Reciprocamente, se for dada uma família de anéis de valorização de Dubrovin, satisfazendo a propriedade da interseção, então existe uma gauge minimal associada, assumindo-se que a valorização de centro tem posto finito. O passo fundamental nesse sentido foi obtermos um teorema de existência de gauges minimais em álgebras centrais simples sobre corpos com uma valorização de posto finito. Além disso, generalizamos para álgebras simples, não necessariamente centrais, um resultado de Tignol e Wadsworth que relaciona gauges com certas funções valorização introduzidas por Morandi em 1989 e que estão associadas aos anéis de valorização de Dubrovin integrais sobre o centro. Como consequência desse último resultado, obtivemos um teorema de existência de gauges em álgebras semi-simples de dimensão finita sobre um corpo com uma valorização de posto 1
Abstract: In this thesis work we study the connection between two theories of noncommutative valuation: Dubrovin valuation rings and gauges. Dubrovin valuation rings were introduced in 1982 as a generalization of invariant valuation rings to Artinian simple rings. Gauges are valuation-like maps that can be defined not only on division algebras, but more generally, on finite-dimensional semisimple algebras over valued fields. Gauges were introduced much more recently in 2010 by Tignol and Wadsworth. Just as for valuations on fields, we can define a ring associated to a gauge, which we call gauge ring. Arithmetic properties of the gauge ring are studied. We show that the gauge ring is always a semi-local order integral over its center. We also describe the gauge ring with respect to composition of gauges and scalar extension. We introduce the concept of minimal gauge on central simple algebras, which are gauges that the degree zero part of the associated graded ring has the least number of simple components. We show that the ring of a minimal gauge is an intersection of a family of Dubrovin valuation rings having the intersection property. The intersection property was introduced by Gräter in 1992. We also proved that if we start with a family of Dubrovin valuation rings having the intersection property, then there exist a minimal gauge associated, assuming that the valuation of the center has finite rank. In this direction, our main result is an existence theorem of minimal gauges on central simple algebra over a field with a finite rank valuation. We also generalize for simple algebras, non-necessarily central, a result of Tignol and Wadsworth which relate gauges with certain value functions introduced by Morandi in 1989. This value functions are associated to Dubrovin valuation rings integral over its center. As a consequence of this last result, we obtain an existence theorem of gauges on finite dimensional semisimple algebras over a field with a rank one valuation
Doutorado
Matematica
Doutor em Matemática
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Laubacher, Jacob C. "Secondary Hochschild and Cyclic (Co)homologies." Bowling Green State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1489422065908758.
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Wagner, David R. "Schur Rings Over Projective Special Linear Groups." BYU ScholarsArchive, 2016. https://scholarsarchive.byu.edu/etd/6089.
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This thesis presents an introduction to Schur rings (S-rings) and their various properties. Special attention is given to S-rings that are commutative. A number of original results are proved, including a complete classification of the central S-rings over the simple groups PSL(2,q), where q is any prime power. A discussion is made of the counting of symmetric S-rings over cyclic groups of prime power order. An appendix is included that gives all S-rings over the symmetric group over 4 elements with basic structural properties, along with code that can be used, for groups of comparatively small order, to enumerate all S-rings and compute character tables for those S-rings that are commutative. The appendix also includes code optimized for the enumeration of S-rings over cyclic groups.
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Bilal, Muhammad. "Codes over rings: maximum distance separability and self-duality." Doctoral thesis, Universitat Autònoma de Barcelona, 2012. http://hdl.handle.net/10803/107703.
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Una parte imporante de la teoría de códigos es la de determinar cotas del número de palabras de un código. Uno de los problemas fundamentales de la teoría de códigos es encontrar códigos con la máxima distancia mínima d. Los investigadores han encontrado diferentes cotas superiores e inferiores para los códigos lineales y no lineales, por ejemplo cotas de Plotkin, Johnson, Singleton, Elias, Linear Programming, Griesmer, Gilbert y Varshamov.
En esta tesis se ha estudiado la cota de Singleton, que es una cota superior de la distancia mínima de un código, y se han definido los códigos Z2Z4-aditivos a distancia máxima separable (MDS). Dos cotas diferentes se presentan en este trabajo en el que se han caracterizado todos los códigos Z2Z4-aditivos a distancia máxima separable con respecto a la cota de Singleton (MDSS) y condiciones en los parámetros para códigos Z2Z4-aditivos a distancia máxima separable con respecto a la cota obtenida a partir del rango (MDSR).
La generación de nuevos códigos ha sido siempre un tema interesante, dando lugar al estudio de las propiedades de estos nuevos códigos generados y a establecer nuevos resultados. Los códigos autoduales son una clase importante de códigos. Hay numerosas construcciones de códigos autoduales a partir de objetos combinatorios. En este trabajo se han dado dos métodos para generar códigos autoduales a partir de esquemas de asociación de clase 3; las construcciones pure y bordered. Con estos dos métodos, se han obtenido códigos binarios autoduales a partir de esquemas de asociación de clase 3 no simétricos y códigos sobre Zk a partir de esquemas de asociación rectangulares.
Borges, Dougherty y Fernández-Córdoba en 2011 presentaron un método para generar nuevos códigos Z2Z4-aditivos autoduales a partir de otros códigos Z2Z4-aditivos autoduales extendiendo su longitud. En este trabajo se ha comprobado si las propiedades como separabilidad, antipodalidad y el tipo del código se mantienen o no cuando se utiliza este método.Bounds on the size of a code are an important part of coding theory. One of the fundamental problems in coding theory is to find a code with largest possible distance d. Researchers have found different upper and lower bounds on the size of linear and nonlinear codes e.g., Plotkin, Johnson, Singleton, Elias, Linear Programming, Griesmer, Gilbert and Varshamov bounds. In this dissertation we have studied the Singleton bound, which is an upper bound on the minimum distance of a code, and have defined maximum distance separable (MDS) Z2Z4 additive codes. Two different forms of these bounds are presented in this work where we have characterized all maximum distance separable Z2Z4-additive codes with respect to the Singleton bound (MDSS) and strong conditions are given for maximum distance separable Z2Z4-additive codes with respect to the rank bound (MDSR). Generation of new codes has always been an interesting topic, where one can study the properties of these newly generated codes and establish new results. Self-dual codes are an important class of codes. There are numerous constructions of self-dual codes from combinatorial objects. In this work we have given two methods for generating self-dual codes from 3-class association schemes, namely pure construction and bordered construction. Binary self-dual codes are generated by using these two methods from non-symmetric 3-class association schemes and self-dual codes from rectangular association schemes are generated over Zk. Borges, Dougherty and Fernández-Córdoba in 2011 presented a method to generate new Z2Z4-additive self-dual codes from the existing Z2Z4-additive selfdual codes by extending their length. In this work we have verified whether properties like separability, antipodality and code Type are retained or not, when using this method.
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Zimmerman, Wendy Cherie. "Association of Pericentrin with the γ Tubulin Ring Complex: a Dissertation." eScholarship@UMMS, 2004. https://escholarship.umassmed.edu/gsbs_diss/122.
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Pericentrin is a molecular scaffold protein. It anchors protein kinases, (PKB, (Purohit, personal communication), PKC, (Chen et al., 2004), PKA Diviani et al., 2000), the γ tubulin ring complex, (γ TuRC) (Zimmerman et al., 2004), and possibly dynein (Purohit et al., 1999) to the spindle pole. The γ TuRC is a ~ 2 MDa complex which binds the minus ends of microtubules and nucleates microtubules in vitro, (Zheng et al., 1995). Prior to this work, nothing was known about the association of the γTuRC with pericentrin. Herein I report the biochemical identification of a large protein complex in Xenopus extracts containing pericentrin, the γ TuRC, and other as yet unidentified proteins. Immunodepletion of γ tubulin results in co-depletion of pericentrin, indicating that virtually all the pericentrin in a Xenopus extract is associated with γ tubulin. However, pericentrin is not a member of the, γ TuRC, since isolated γ TuRCs do not contain pericentrin. The association of pericentrin with the γ TuRC is readily disrupted, resulting in two separable complexes, a small pericentrin containing complex of approximately 740 KDa and the the γ TuRC, 1.9 MDa in Xenopus. Co overexpression/ coimmunoprecipitation and yeast two hybrid studies demonstrate that pericentrin binds the γTuRC through interactions with both GCP2 and GCP3. When added to Xenopus mitotic extracts, the GCP2/3 binding domain uncoupled γ TuRCs from centrosomes, inhibited microtubule aster assembly and induced rapid disassembly of pre-assembled asters. All phenotypes were significantly reduced in a pericentrin mutant with diminished GCP2/3 binding, and were specific for mitotic centro somal asters as I observed little effect on interphase asters or on asters assembled by the Ran-mediated centrosome-independent pathway. Overexpression of the GCP2/3 binding domain of pericentrin in somatic cells perturbed mitotic astral microtubules and spindle bipolarity. Likewise pericentrin silencing by small interfering RNAs in somatic cells disrupted γ tubulin localization and spindle organization in mitosis but had no effect on γ tubulin localization or microtubule organization in interphase cells. Pericentrin silencing or overexpression induced G2/antephase arrest followed by apoptosis in many but not all cell types. I conclude that pericentrin anchoring of γ tubulin complexes at centrosomes in mitotic cells is required for proper spindle organization and that loss of this anchoring mechanism elicits a checkpoint response that prevents mitotic entry and triggers apoptotic cell death. Additionally, I provide functional and in vitro evidence to suggest that the larger pericentrin isoform (pericentrin B/ Kendrin) is not functionally homologous to pericentrin/pericentrin A in regard to it's interaction with the γ TuRC.
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Costa, Cano Francisco José. "Estudio de las relaciones entre propiedades de un anillo y sus anillos de matrices infinitas." Doctoral thesis, Universidad de Murcia, 2006. http://hdl.handle.net/10803/10964.
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Esta tesis se propone el estudio de la relación entre propiedades de un anillo R y propiedades de algunos de sus anillos de matrices infinitas. Así, un resultado "modelo" sobre este problema será de la forma: "Sean P y Q dos propiedades. El anillo R cumple la propiedad P si y sólo cierto anillo de matrices infinitas, S, sobre R, cumple la propiedad Q.Los tipos principales de anillos de matrices infinitas sobre algún anillo R consideradas en este trabajo son, primero, aquellas que tienen un número finito de entradas no nulas en cada fila, conocidas como "matrices de filas finitas" y, segundo, aquellas que tienen en cada fila y cada columna un número finito de entradas no nulas, conocidas como "matrices de filas y columnas finitas.The purpose of this thesis is the study of the relationship between properties of a ring R and properties of some of its infinite matrix rings.A standard result in this topics may be stated as: "Let P and Q two properties. The ring R satisfies property P if and only if certain infinite matrix ring, S, over R, satisfies property Q.The principal infinite matrix types considered in this thesis are, first, those matrices that have a finite number of nonzero entries in each row, known as "row finite matrices", and second, those matrices that have a finite number of nonzero elements in each row and each column, known as "row and column finite matrices".
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Caprio, Joseph M., Harold C. Fritts, Richard L. Holmes, David M. Meko, and Deborah L. Hemming. "A Chi-Square Test for the Association and Timing of Tree Ring-Daily Weather Relationships: A New Technique for Dendroclimatology." Tree-Ring Society, 2003. http://hdl.handle.net/10150/262549.
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This study introduces a new analytical procedure based on the chi-square (x²) statistic to evaluate tree- ring weather relationships. An iterative x² method, developed previously for relating annual crop production to daily values of meteorological measurements, is applied to tree-ring data and compared to results obtained from correlation and bootstrapped response function analyses. All three analytical procedures use a southern Arizona chronology (Pinus arizonica Engelm.) and the latter two use monthly average meteorological data. The x² analysis revealed most of the relationships exhibited by the correlation and response function analyses as well as new linear and nonlinear associations. In addition, cardinal values were obtained that define daily thresholds of the meteorological variables at which the limitation to growth becomes significant. Some of the associations are plausible from the physical system but require more study to confirm or refute a real cause and effect. A few associations appear to be too late in the season or too early in the previous year to affect ring width. We recommend that this x² technique be added to the existing dendroclimatic procedures because it reveals many more possible cause and effect relationships.
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Silva, Viviane Moretto da. "Algebras de Lie finitamente apresentaveis." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306934.
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Orientador: Dessislava Hristova KochloukovaDissertação (mestrado) - Universidade Estadual de Campinas. Instituto de Matematica, Estatistica e Computação Científica
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Resumo: Nesta dissertação de mestrado, estudamos propriedades de álgebras de Lie. As Álgebras de Lie têm grande importância nao somente na teoria de álgebras não associativas, elas surgem também em geometria, topologia e no estudo da teoria de grupos por exemplo. As definições e resultados básicos sobre álgebras de Lie estão inclusos no Capítulo 2. Para esta parte do trabalho, utilizamos os livros [1] e [2]. O nosso enfoque foi sobre álgebras universais envelopantes, mergulhando assim a álgebra de Lie em álgebras associativas (Seções 2.4, 2.5 e 2.6). O objetivo principal da dissertação foi estudar o artigo [4], ¿Finite presentation of abelian-by-finite dimensional Lie algebras¿, que classifica álgebras de Lie finitamente apresentáveis (no sentido de serem definidas por número finito de geradores e relações) que são extensões de ideal abeliano por álgebra de Lie de dimensão finita. Definimos álgebras de Lie livres na seção 2.7.Tratam-se de objetos na categoria de álgebras de Lie que satisfazem propriedade universal semelhante a definição de grupos livres. A classificação de álgebras de Lie que são extensões de ideal abeliano por álgebra de Lie de dimensão finita usa teoria de módulos Noetherianos. No Capítulo 1 incluímos resultados básicos sobre módulos, em particular estudamos módulos Noetherianos, não necessariamente sobre anéis comutativos (para este estudo utilizamos [9]), embora alguns resultados sejam válidos somente no caso onde o anel básico é comutativo (caso do Teorema da Base de Hilbert 1.31 no Capítulo 1). No final, nos Capítulos 3 e 4, explicamos de maneira bem minuciosa (com mais 6 detalhes que o original) o resultado principal de [4], que 'e apresentado na página 42: Proposicão 3.2: Seja L uma álgebra de Lie finitamente gerada sobre o corpo K. Suponha que L tenha um ideal abeliano A tal que L/A tem dimensão finita como espaço vetorial. Seja R álgebra universal envelopante de L/A. Suponha também que o quadrado tensorial A X A é finitamente gerado como R-módulo sobre a ação diagonal. Então L é finitamente apresentável. Os métodos da demonstração de 3.2 envolvem muitos cálculos com relações em L para mostrar que um conjunto finito E 'e suficiente para gerar todas as relações em L. Embora os cálculos sejam muitos, a técnica principal 'e a indução e a Identidade de Jacobi. A teoria de módulos Noetherianos também foi muito utilizada
Abstract: In this work we study the classification of finitely presented abelian-by-finite dimensional Lie algebras given in [4]. If L is a Lie algebra, an extension of an abelian ideal A by a finite dimensional Lie algebra L/A then L is finitely presented if and only if A X A is finitely generated as U(L/A)-module via the diagonal action, where U(L/A) is the universal enveloping algebra of L/A. We study in detail the result that finite generation of A X A over U(L/A) implies finite presentability of L
Mestrado
Matematica
Mestre em Matemática
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Bastian, Nicholas Lee. "Terwilliger Algebras for Several Finite Groups." BYU ScholarsArchive, 2021. https://scholarsarchive.byu.edu/etd/8897.
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In this thesis, we will explore the structure of Terwilliger algebras over several different types of finite groups. We will begin by discussing what a Schur ring is, as well as providing many different results and examples of them. Following our discussion on Schur rings, we will move onto discussing association schemes as well as their properties. In particular, we will show every Schur ring gives rise to an association scheme. We will then define a Terwilliger algebra for any finite set, as well as discuss basic properties that hold for all Terwilliger algebras. After specializing to the case of Terwilliger algebras resulting from the orbits of a group, we will explore bounds of the dimension of such a Terwilliger algebra. We will also discuss the Wedderburn decomposition of a Terwilliger algebra resulting from the conjugacy classes of a group for any finite abelian group and any dihedral group.
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Kinuthia, Wanyee. "“Accumulation by Dispossession” by the Global Extractive Industry: The Case of Canada." Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/30170.
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This thesis draws on David Harvey’s concept of “accumulation by dispossession” and an international political economy (IPE) approach centred on the institutional arrangements and power structures that privilege certain actors and values, in order to critique current capitalist practices of primitive accumulation by the global corporate extractive industry. The thesis examines how accumulation by dispossession by the global extractive industry is facilitated by the “free entry” or “free mining” principle. It does so by focusing on Canada as a leader in the global extractive industry and the spread of this country’s mining laws to other countries – in other words, the transnationalisation of norms in the global extractive industry – so as to maintain a consistent and familiar operating environment for Canadian extractive companies. The transnationalisation of norms is further promoted by key international institutions such as the World Bank, which is also the world’s largest development lender and also plays a key role in shaping the regulations that govern natural resource extraction. The thesis briefly investigates some Canadian examples of resource extraction projects, in order to demonstrate the weaknesses of Canadian mining laws, particularly the lack of protection of landowners’ rights under the free entry system and the subsequent need for “free, prior and informed consent” (FPIC). The thesis also considers some of the challenges to the adoption and implementation of the right to FPIC. These challenges include embedded institutional structures like the free entry mining system, international political economy (IPE) as shaped by international institutions and powerful corporations, as well as concerns regarding ‘local’ power structures or the legitimacy of representatives of communities affected by extractive projects. The thesis concludes that in order for Canada to be truly recognized as a leader in the global extractive industry, it must establish legal norms domestically to ensure that Canadian mining companies and residents can be held accountable when there is evidence of environmental and/or human rights violations associated with the activities of Canadian mining companies abroad. The thesis also concludes that Canada needs to address underlying structural issues such as the free entry mining system and implement FPIC, in order to curb “accumulation by dispossession” by the extractive industry, both domestically and abroad.
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Kwei, Shiue Wen, and 薛文魁. "Skew Derivations On Associative Rings." Thesis, 1994. http://ndltd.ncl.edu.tw/handle/76709976206664799724.
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McConnell, N. R(Nicholas Richard). "Studies in radical theory for restricted classes of rings." Thesis, 1990. https://eprints.utas.edu.au/20170/1/whole_McConnellNicholasRichard1991_thesis.pdf.
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This thesis is a study of radical ideals in restricted domains of
associative rings.
The first chapter introduces a generalisation of the concept of strictness,
and studies, for a given radical class, the class of rings for which the radical is
hereditary and/or strict (in the general sense). This leads to some results on
embedding radical classes in generalised strict radical classes, and on degrees of
hereditariness of radical classes.
In the second chapter, the ideals of a ring which can be radical ideals are
studied, with characterisations being given for Dedekind domains and some of
their extension rings. This characterises radical ideals for a fairly wide class of
integral domains, and thus goes some way toward characterising supernilpotent
radical ideals of commutative rings.
In the third chapter, a study is made of radical classes of commutative
rings, with a characterisation being given of the strongly hereditary strict
radicals, and the implications of restricting to commutativity are considered for
some other results and problems. There is also an investigation of the permanent
radical — that is, the part of the radical of a ring which remains as part of the
radical of any extension — for more general classes of rings.
The thesis thus gives an insight into the behaviour of radical classes
within single rings rather than globally, which gives us more information about
the nature of radical classes.
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Reynders, Schalk Willem. "Regulariteite in ringe." Thesis, 2014. http://hdl.handle.net/10210/11938.
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Shardha, S. "On certain non-associative rings and algebras with commutators in the nuclei." Thesis, 1986. http://localhost:8080/xmlui/handle/12345678/4720.
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(9910865), Melanie Soo Chin. "Towards a reinterpretation of the radical theory of associative rings using base radical and base semisimple class constructions." Thesis, 2004. https://figshare.com/articles/thesis/Towards_a_reinterpretation_of_the_radical_theory_of_associative_rings_using_base_radical_and_base_semisimple_class_constructions/13417001.
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"This research aims to refresh and reinterpret the radical theory of associative rings using the base radical and base semisimple class constructions. It also endeavours to generalise some results about ideals of rings in terms of accessible subrings. A characterisation of accessible subrings is included. By applying the base radical and base semisimple class constructions to many of the known results in established radical theory a number of gaps are uncovered and closed, with the goal of making the theory more accessible to advanced undergraduate and graduate students and mathematicians in related fields, and to open up new areas of investigation. After a literature review and brief reminder of algebra rudiments, the useful properties of accessible subrings and the U and S operators independent from radical class connections are described. The section on accessible subrings illustrates that replacing ideals with accessible subrings is indeed possible for a number of results and demonstrates its usefulness. The traditional radical and semisimple class definitions are included and it is shown that the base radical and base semisimple class constructions are equivalent. Diagrams illustrating the constructions support the definitions. From then on, all radical and semisimple classes mentioned are understood to have the base radical and base semisimple class form. Subject to the constraints of this work, many known results of traditional radical theory are reinterpreted with new proofs, illustrating the potential to simplify the understanding of radical theory using the base radical and base semisimple class constructions. Along with reinterpreting known results, new results emerge giving further insight to radical theory and its intricacies. Accessible subrings and the U and S operators are integrated into the development. The duality between the base radical and base semisimple class constructions is demonstrated in earnest. With a measure of the theory presented, the new constructions are applied to examples and concrete radicals. Context is supported by establishing the relationship between some well-known rings and the radical and related classes of interest. The title of the thesis, Towards a Reinterpretation of the Radical Theory of Associative Rings Using Base Radical and Base Semisimple Class Constructions, reflects the understanding that reinterpreting the entirety of radical theory is beyond the scope of this work. The conclusion includes an outlook listing further research that time did not allow."
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(9788648), Guy Cooke. "On lower radical type constructions." Thesis, 2010. https://figshare.com/articles/thesis/On_lower_radical_type_constructions/13456742.
Full textAbstract:
This research is essentially an investigation into lower radical type construction and the consequences thereof. Dealing primarily in associative rings, the aim of this thesis is to construct - and investigate - a generalised lower radical type construction that encapsulates McDougall's base radical class construction and Stewart's strict radical class construction. Beginning with some preliminary results and a brief account of the lower radical (type) constructions in associative rings, we develop the basic concepts and notations used throughout the investigation. After determining a number of substructures suitable for use in our lower radical type construction (a ϱ-radical class), we go on to examine some of the similarities, differences and properties of the ϱ-radical class relative to those of the existing contructions.
In the lattice of all radical classes, we focus on the connections that both the base and strict radical constuctions have respectively to two specific ϱ-radical constructions. Moreover, we determine that all such ϱ-radicals are contained in particular non-trivial radical classes, and subsequently position these against the so called concrete radicals in the lattice of all radical classes. We also demonstrate that the structure of a lattice of ϱ-radical classes is partially dependent on the generating class, and thus not fixed in terms of construction.
In considering the dual construction to the ϱ-radical class, we learn that unlike the ϱ-radical construction always generating a radical class, the dual construction need not always generate a semisimple class. We consider some of the cases in which the dual is semisimple, and give a sufficient condition to determine the ϱ-properties that so generate a ϱ-semisimple class. Whilst on the subject of semisimple classes, we generalise the notion of the strongly R-semisimple ring, and explore when a class of such rings is a radical class.
The thesis concludes by generalising the ϱ-radical construction to suit an arbitrary GS-category. In doing so we validate the ϱ-radical construction in structures such as groups, near-rings, nonassociative rings, any variety of rings or algebras, (Hausdorff) topological groups and rings, and vector value spaces to name just a few. This has certainly opened a door for further investigation, in these and possibly other branches of mathematics.
The simplicity and flexibility of the theory developed in this research provides an accessibility that may have wider applications in algebra -- Abstract.
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Juang, Ming-Yu, and 莊明裕. "The Association between Hypertension andWhite Ring around Iris." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/10041331509815376469.
Full textAbstract:
碩士建國科技大學
機電光系統研究所
94
The elongation of the average life-span of Taiwan nationals leads Taiwan to be becoming an advanced age society.The body functions of the middle-age and aged people are also degenerating. Hence, the chronic diseases, especially cardiovascular diseases, have been becoming the great threatens to these ages. Hypertension is one kind of common diseases, and it is also a very important reason causing cardiovascular diseases and even death in developed countries. Due to hypertension itself having no obvious symptoms, people are acknowledged while they fall ill seriously. Therefore, hypertension is called an invisible killer. Our study was to collect the data from 48 test-acceptors,average age 50.6±11.1,who were divided into two groups, hypertension and non-hypertension. The test-acceptors were examined with iris detector to check whether there is any spray around their periphery iris. We counted the numbers of the two groups, and then analyzed the data by Chi-square Test . The result was P<0.001,it would indicate the obvious association between hypertension and the producing of spray around the periphery iris. The aim of this study was to take the non-invasive and the non-medicine human body examination based on preventive medicine. We encourage the elder people and even those who don’t like to take health examination in the hospital to observe their periphery iris with a pen light in ordinary. The purposes were to beforehand prevent hypertension producing by completing the promotion of the hygienic condition and to reach the goal of early discovery early treatment.
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Restrepo, Blandon Fredy Alexander. "Operadores diferenciales de tipo de Lunts-Rosenberg de álgebras de matrices polinómicas, álgebras de caminos y álgebras de matrices triangulares formales." Doctoral thesis, 2019. http://hdl.handle.net/11086/11749.
Full textAbstract:
Tesis (Doctor en Matemática)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2019.En este trabajo estudiamos el anillo filtrado de operadores diferenciales sobre álgebras no conmutativas D(A) , formulado por primera vez de manera intrínseca por Lunts y Rosenberg. Describimos el anillo de operadores diferenciales para las álgebras de matrices polinómicas Mm(C[X]), las álgebras de caminos sobre un carcaj finito, acíclico y conexo Γ(Q), y las álgebras de matrices triangulares formales TL. Cerramos este trabajo exponiendo nuevos operadores diferenciales que no provienen de las derivaciones, obteniendo así, nuevos objetos de estudio
In this work, we study the filtered ring of differential operators on non-commutative algebras D(A), formulated for the first time in an intrinsic way by Lunts and Rosenberg. We describe the ring of differential operators for the polynomial matrix algebras Mm(C[X]) , the algebras of paths on a finite, acyclic and connected quiver Γ(Q), and the algebras of formal triangular matrices TL. We close this work, exposing new differential operators that do not come from derivations, thus obtaining new objects of study.
Fil: Restrepo Blandon, Fredy Alexander. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.
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Li, Boyu. "Ring/Chain versus Network: Architecture Induced by Self- versus Pairwise-Association of Telechelic Polymers." Thesis, 2016. https://thesis.library.caltech.edu/9805/1/Boyu%20Li%27s%20thesis.pdf.
Full textAbstract:
Non-covalent associations, including hydrophobic interaction or ionic interaction for self-association, and metal coordination or hydrogen-bonding for complementary-association, have been widely used as key interactions in supramolecules formation with telechelic associative polymers. And a specific application of long associative telechelic polymers has been developed by our group for the mist-control and drag-reduction of liquid fuels. During the research on this project, self- and pairwise-associative telechelic polymers are able to be compared for the first time, and are shown to display distinct associative patterns. In order to design materials with the desired properties, it is imperative to understand the relationships between polymer chemical structure and their topology and dynamics.
In this thesis, self-associative telechelic polymer refers to α,ω-di(isophthalic acid) polycyclooctadiene (DA-PCOD), which can associate with itself through its acid ends. When tertiary amine-ended polymer is added into the mixture, isophthalic acid preferably associates pairwisely with tertiary amine due to the higher binding strength of charge-assisted hydrogen bond. And the 1:1 molar ratio mixture of α,ω-di(isophthalic acid) and α,ω-di(di(tertiary amine)) PCOD (DA/DB-PCOD) is named as pairwise-associative telechelic polymers. DA-PCOD is capable of multimeric association via directional hydrogen bonding due to the specific chemical structure of the isophthalic acid end, while DA/DB-PCOD exhibits dynamics that strikingly resembles that for linear covalent polymers. Temperature determines the binding strength of self- and pairwise- end association, and furthermore, the fraction of unbound ends and the distribution and topology of formed supramolecules/aggregates. Polymer length affects the dynamics of DA-PCOD mainly through determining the concentration of the end groups. And the net effect of chain length on the dynamics of DA/DB-PCOD is non-monotonic and varies with the specific temperature and concentration. The knowledge of structure-property relationships obtained from this work will enable future design of end group entities and other properties of these associative telechelic polymers for their specific applications.