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1

Grimley, Matthew. "Citizenship, community and the Church of England : Anglican theories of the State, c.1926-1939." Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.286655.

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2

Rocha, Renato Gomes de Araujo. "Teorias da Conduta: uma análise crítica." Universidade do Estado do Rio de Janeiro, 2014. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=7485.

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Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro
Neste trabalho foram analisadas e comparadas as principais teorias da conduta. Com isso buscou-se não apenas aprofundar um debate frequentemente mediado pelos manuais, mas também, por meio do recurso aos aportes críticos da bibliografia latino-americana, verificar se a concepção ontológica de conduta é de fato a mais limitadora ao poder punitivo. Parte do eixo analítico deste trabalho passa pelo estudo da articulação entre o respeito à estrutura lógico-objetiva da conduta humana como base de sucessivas valorações e a função limitadora da conduta. Com isso, pretende-se debater se a minimização dessa estrutura lógico-objetiva, acarretando a um acréscimo potencial de uma normativização do direito penal, representaria uma maior exposição do sujeito ao poder punitivo. A partir do conceito de praxis, como desenvolvido por Lukács, busca-se paralelamente uma base filosófica que não se esgote na compartimentalização jurídica. Trata-se de uma corrente que reivindica criticamente a herança teórica das principais contribuições filosóficas ocidentais, desde proposições aristotélicas, passando pelos conceitos hegelianos, chegando ao debate sobre objetificação hegeliano-marxista.
This study analyzed and compared the major theories about human conduct. The intent behind this was to not only deepen a debate often mediated by the manuals, but also, through the use of the critical contributions of Latin-american literature, to verify if the ontological conception of conduct is indeed the most limiting of punitive power. Part of the analytical axis of this work involves the study of the relationship between the respect for logical-objective structures of human conduct, as the basis of successive value attributions, and conduct in its limiting function. With this, we intend to debate whether the reduction of recognition of logical-objective structures, leading to increased potential for normative aspects of criminal law, represents a greater exposure of the subject to punitive power. From the concept of praxis, as developed by Lukacs, we aim to find a philosophical basis that is not exhausted in legal compartmentalization. This theoretical path critically claims the heritage of major Western philosophical contributions, from Aristotelian propositions through the Hegelian concepts, reaching the debate on Hegelian-Marxist objectification.
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3

Redman, Lynn. "Algebraic Methods for Proving Geometric Theorems." CSUSB ScholarWorks, 2019. https://scholarworks.lib.csusb.edu/etd/923.

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Algebraic geometry is the study of systems of polynomial equations in one or more variables. Thinking of polynomials as functions reveals a close connection between affine varieties, which are geometric structures, and ideals, which are algebraic objects. An affine variety is a collection of tuples that represents the solutions to a system of equations. An ideal is a special subset of a ring and is what provides the tools to prove geometric theorems algebraically. In this thesis, we establish that a variety depends on the ideal generated by its defining equations. The ability to change the basis of an ideal without changing the variety is a powerful tool in determining a variety. In general, the quotient and remainder on division of polynomials in more than one variable are not unique. One property of a Groebner basis is that it yields a unique remainder on division. To prove geometric theorems algebraically, we first express the hypotheses and conclusions as polynomials. Then, with the aid of a computer, apply the Groebner Basis Algorithm to determine if the conclusion polynomial(s) vanish on the same variety as the hypotheses.
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4

Cormack, Alistair. "Yeats and Joyce : cyclical theories of history and the reprobate tradition of Irish idealism in Ulysses, A Vision and Finnegans Wake." Thesis, University of East Anglia, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.405348.

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5

Hoffman, Douglas J. "A Coloring Theorem for Inaccessible Cardinals." Ohio University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1385056127.

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6

Pau, Plana Jordi. "Ideals finitament generats i decreixement de funcions analítiques i acotades." Doctoral thesis, Universitat Autònoma de Barcelona, 2001. http://hdl.handle.net/10803/3090.

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7

Potter, Matthew Charles. "The critical turn in British art : the influences of German idealism on British art critics, theorists and practitioners in the late nineteenth century." Thesis, Birkbeck (University of London), 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.416017.

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8

Bantekas, Evangelos. "Vom subjektiven zum objektiven Gedanken." Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/19510.

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Hegel führt die traditionelle formale Logik, wie sie in Kants Konzept der reinen allgemeinen Logik ihre für ihn abschließende Gestalt erfahren hat, innerhalb seiner Systematik auf die Psychologie der produktiven Einbildungskraft und des Denkens zurück. Kants Konzeption der transzendentalen Logik, und mit ihr die neuzeitliche Erkenntnistheorie, wird aus gesamtsystematischer Hinsicht in der Philosophie des subjektiven Geistes verortet, und insbesondere in der Phänomenologie des Geistes und der Psychologie der Anschauung und Vorstellung. In logischer Hinsicht leistet Kant nach Hegel nur eine Übersetzung phänomenologischer Inhalte der psychologischen Vorstellung in relativ unterentwickelte und isolierte objektivlogische Strukturen (reine Reflexions- und wesentliche Verhältnisbestimmungen), wodurch er über den psychologischen Reflex des Begriffs nicht hinauskommt. Der logische Inhalt bzw. der objektive Gedanke dagegen basiert in seiner formalen Dimension auf die Realisierung des Begriffs im Prozess der endlichen Teleologie, aus deren Perspektive auch phänomenologische und logische Dimensionen von Struktur- und Verhältnisbestimmungen differenziert werden können (Inhalte der kontemplative Erwägung der Konstruktionsbedingungen des unausgeführten subjektiven Zwecks im ersten Fall, Funktionalität von Strukturverhältnissen im Prozess der Ausführung des subjektiven Zwecks im zweiten Fall). Der logische Inhalt ist konkret im Vergleich zum phänomenologischen Inhalt der psychologischen Vorstellung und abstrakt im Vergleich zum realsystematischen Inhalt als Korrelat der absoluten Methode.
Within his system Hegel relegates traditional formal logic, as it found its fulfillment in Kant´s concept of pure general logic, to the psychology of productive imagination and thought. Kant´s conception of transcendental logic, and with it a modern epistemological standpoint more generally, is also allocated in the philosophy of subjective spirit, and more specifically in the phenomenology and the psychology of intuition and representation. From a logical standpoint Kant does not, according to Hegel, go beyond translating phenomenological contents of the psychological representation into the relatively simple structures of the determinations of reflection and essential relations, thereby staying within the realm of the mere psychological reflex of the concept. Determinate logical content or objective thought on the contrary is based in its formal dimension on the actualization of the concept in the process of finite teleology. From this perspective it is possible to coherently distinguish between phenomenological and logical dimensions of structural and relational determinations (contents of the contemplative assessment of the conditions of construction of the yet unexecuted subjective finite end on the one hand, functionality of structural relations in the process of executing this end on the other). The logical content is concrete compared to the phenomenological one and abstract compared to the content of the real parts of the system as the correlate of absolute logical method.
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9

Van, Zyl Jacobus Visser. "On the Latimer-MacDuffee theorem for polynomials over finite fields." Thesis, Stellenbosch : University of Stellenbosch, 2011. http://hdl.handle.net/10019.1/6581.

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Thesis (PhD (Mathematical Sciences))--University of Stellenbosch, 2011.
Includes bibliography.
ENGLISH ABSTRACT: Latimer & MacDuffee showed in 1933 that there is a one-to-one correspondence between equivalence classes of matrices with a given minimum polynomial and equivalence classes of ideals of a certain ring. In the case where the matrices are taken over the integers, Behn and Van der Merwe developed an algorithm in 2002 to produce a representative in each equivalence class. We extend this algorithm to matrices taken over the ring Fq[T] of polynomials over a finite field and prove a modified version of the Latimer-MacDuffee theorem which holds for proper equivalence classes of matrices.
AFRIKAANSE OPSOMMING: Latimer & MacDuffee het in 1933 bewys dat daar 'n een-tot-een korrespondensie is tussen ekwivalensieklasse van matrikse met 'n gegewe minimumpolinoom en ekwivalensieklasse van ideale van 'n sekere ring. In die geval waar die matrikse heeltallige inskrywings het, het Behn en Van der Merwe in 2002 'n algoritme ontwikkel om verteenwoordigers in elke ekwivalensieklas voort te bring. Ons brei hierdie algoritme uit na die geval van matrikse met inskrywings in die ring Fq[T] van polinome oor 'n eindige liggaam en ons bewys 'n gewysigde weergawe van die Latimer-MacDuffee stelling wat geld vir klasse van streng ekwivalente matrikse.
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10

Dusepulchre, Gaëlle. "Politique européenne de coopération au développement et relations extérieures: des droits de l'homme à la bonne gouvernance, impact de l'interdépendance du droit et du politique sur le choix des instruments de régulation." Doctoral thesis, Universite Libre de Bruxelles, 2008. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210587.

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L'étude a porté sur deux outils élaborés par l’Union européenne à l'appui de ses politiques d'allocation d'aide extérieure au bénéfice principalement d'Etats en développement et participant à sa stratégie de promotion du respect de droits de l’homme dans les Etats tiers. Il s'agit du mécanisme de conditionnalité démocratique d’une part, et de la doctrine fondée sur le concept de gouvernance d’autre part. L'une des principales critiques que la doctrine adresse à l’Union au sujet de sa politique de conditionalité est son incapacité à répondre à l’une des attentes fondamentales qui la sous-tend, à savoir :la naissance d’une politique d’aide extérieure détachée des considérations géopolitiques et visant à protéger et promouvoir efficacement les droits de l’homme. Dans la mesure où la doctrine en attribue en général la responsabilité à l’absence de clarté et de prévisibilité du mécanisme de la conditionnalité démocratique, cette critique eut dû conduire à l’élaboration d’un régime davantage juridicisé. Or, l'émergence de la doctrine fondée sur le concept de gouvernance révèle que l’Union n’a pas opté pour une telle solution. C’est alors que, divisant mon étude en deux parties, la première affectée à l’étude du mécanisme conditionnel et la seconde affectée à l’étude de la doctrine de gouvernance, je me suis interrogée sur les raisons pour lesquelles l’Union avait pu choisir de recourir d’abord à un appel au droit, et ensuite à une repolitisation partielle de son mécanisme. Prenant appui sur une étude des documents officiels des institutions européennes, de la pratique de l'Union et des théories des relations internationales, l'étude tend à révéler les atouts et les limites théoriques de chacune de ces stratégies déstinées à suciter des réformes particulières dans les Etats partenaires de l’Union.Il apparaîtra que l’appel au droit opéré dans le cadre du mécanisme de conditionnalité répondait à des besoins et à une logique spécifiques lors de son institution, mais que la forme juridicisée du mécanisme conditionnel tel qu’institué se heurtait à diverses limites. La doctrine fondée sur le concept de gouvernance, dans le même temps qu’elle acte ces limites et tend à les dépasser, amène à de nouveaux questionnements.

The study related to both EU tools, affecting its external aid policies and contributing to its human rights strategy :conditionality and governance. One of the main critic that the doctrine addresses to EU conditionality, is its incapacity to lead to an external aid free of geopolitical considerations and acting to protect and promote effectively the human rights. The doctrine explains this weakness by pointing out the mechanism of conditionality’s lack of clearness and previsibility. Despite this critic is pleading for a more legalized mechanism, the governance strategy reveals that the Union did not choose such a solution.Then, dividing the study into two parts, the first assigned to conditional mechanism and the second assigned to governance, I’m asking the reason why a less legalized mecanism succeeded to conditionality. Based on cooperation agreements, strategic orientations, EU practice and the international relations theories, the study tends to reveal the assets and limits of the two strategies. It appears that the legalization process of conditionality can be explained by specific needs but it encountered various limits. At the same times, while strategy based on Governance adresses some of them, this new tool reveals new questions.


Doctorat en droit
info:eu-repo/semantics/nonPublished

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11

Zoalroshd, Seyed. "On Spectral Properties of Single Layer Potentials." Scholar Commons, 2016. http://scholarcommons.usf.edu/etd/6445.

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We show that the singular numbers of single layer potentials on smooth curves asymptotically behave like O(1/n). For the curves with singularities, as long as they contain a smooth sub-arc, the resulting single layer potentials are never trace-class. We provide upper bounds for the operator and the Hilbert-Schmidt norms of single layer potentials on smooth and chord-arc curves. Regarding the injectivity of single layer potentials on planar curves, we prove that among single layer potentials on dilations of a given curve, only one yields a non-injective single layer potential. A criterion for injectivity of single layer potentials on ellipses is given. We establish an isoperimetric inequality for Schatten p−norms of logarithmic potentials over quadrilaterals and its analogue for Newtonian potentials on parallelepipeds.
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12

Foufas, Nikolaos. "Le concept d’aliénation de Rousseau à Marx : continuités et transformations." Thesis, Paris 10, 2015. http://www.theses.fr/2015PA100103/document.

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La présente étude s’interroge sur le concept d’aliénation, et plus spécifiquement sur sa genèse, son déploiement, son histoire particulière, ses configurations complexes, ses multiples transformations. Trois auteurs sont privilégiés : Rousseau, Hegel, Marx. La tentative d’examiner la notion d’aliénation dans sa forme rousseauiste, hégélienne et jeune-marxienne, a comme point de départ la critique d’Althusser selon laquelle ce concept relèverait d’une vision abstraite, métaphysique, de l’histoire et de l’activité des agents humains. D’après Althusser, l’aliénation est en effet l’expression humaniste d’une philosophie du retour aux origines et de la réunion avec une essence humaine qui se serait perdue. La philosophie de l'aliénation contractuelle (comme fondement de l’institution d’une communauté politique chez Rousseau), la mise en question de la positivité historique dans les écrits du jeune Hegel, et finalement la critique du travail aliéné forgée par le jeune Marx dans ses Manuscrits de 1844, ne seraient-elles toutes au fond que des variations autour d’une même conception essentialiste de l’histoire humaine ? S'écartant d'une telle disqualification indifférenciée, la thèse se propose de mettre en valeur la réflexion originale et singulière que chacun de ces trois auteurs élabore au sujet de l’aliénation, tout en essayant de mettre en lumière ce qu’ils partagent, malgré leurs différences. Car en parlant d'aliénation, il s'agit toujours d'interroger la perte mutilante d’un rapport à soi, à autrui et au monde socialement induite. Et il s'agit toujours aussi de concevoir des conditions historiques jugées dégradantes que l'on doit pouvoir dépasser. En d’autres termes, ce travail se propose de montrer non seulement que l’aliénation ne se réduit pas à une notion abstraite et naïvement humaniste, mais qu’elle forme également un repère incontournable, dès lors qu’elle prend au sérieux la tâche de penser l’impossibilité, pour certains groupes ou certaines classes sociales, de se réaliser et de s'épanouir, sur fond d'une privation durable de ce que peuvent apporter des rapports à soi, aux autres et au monde suffisamment riches et variés
This study examines the concept of alienation, and focuses more specifically on its genesis, its deployment, its particular history, its complex configurations, its multiple transformations. Three authors are highlighted: Rousseau, Hegel, Marx. The attempt to examine the concept of alienation in the forms that Rousseau, Hegel and the young Marx give it, has as its starting point the criticism of Althusser according to whom this concept rises from an abstract, metaphysical vision of history and from the activity of human agents. According to Althusser, alienation is indeed the humanistic expression of a philosophy of the return to the origins and of a reunion with a human essence that might have been lost. The philosophy of contractual alienation (as the basis for the institution of a political community in Rousseau), the questioning of the historical positivity in the writings of the young Hegel, and finally the critique of alienated labor forged by the young Marx in his Manuscripts of 1844, would they basically all be variations around the same essentialist conception of human history? Diverging from such an undifferentiated disqualification, the thesis proposes to develop the original and singular reflection that each one of these three authors is developing on the subject of alienation, while trying to highlight what they share, despite their differences. Because, speaking of alienation, is always here to question the socially induced mutilating loss of a relation to oneself, to others and to the world. And it is also always a subject to conceive historical conditions considered degrading that must be overcome. In other words, this study intends to not only show that alienation cannot be reduced to an abstract and naively humanist concept, but that it also forms a key benchmark, since it takes seriously the task of thinking of the impossibility for certain groups or certain social classes to achieve self-realization and thrive, amid a sustained deprivation of what can be provided by sufficiently rich and varied relations to oneself, to others and to the world
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13

BERNARDINO, Adriano Thiago Lopes. "Contribuições à teoria multilinear de operadores absolutamente somantes." Universidade Federal de Pernambuco, 2016. https://repositorio.ufpe.br/handle/123456789/17977.

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Submitted by Irene Nascimento (irene.kessia@ufpe.br) on 2016-10-11T18:36:34Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Tese Adriano Thiago.pdf: 1085326 bytes, checksum: 498b2bcfd47961466edce3360e11a858 (MD5)
Made available in DSpace on 2016-10-11T18:36:34Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Tese Adriano Thiago.pdf: 1085326 bytes, checksum: 498b2bcfd47961466edce3360e11a858 (MD5) Previous issue date: 2016-06-17
Neste trabalho estudamos algumas extens˜oes do conceito de operadores multilineares absolutamente somantes, generalizamos alguns resultados conhecidos e respondemos parcialmente alguns problemas abertos. Para a classe das aplica¸c˜oes absolutamente (p; q; r)-somantes, obtemos alguns resultados de coincidˆencia e inclus˜ao e mostramos que o ideal de polinˆomios absolutamente (p; q; r)-somantes n˜ao ´e corente, de acordo com a no¸c˜ao de ideais coerentes devida a D. Carando, V. Dimant e S. Muro. Para contornar esta falha, introduzimos o conceito de aplica¸c˜oes m´ultiplo (p; q; r)-somantes e mostramos que, com essa nova abordagem, o ideal de polinˆomios m´ultiplo (p; q; r)- somantes ´e coerente e compat´ıvel com o ideal de operadores lineares absolutamente (p; q; r)-somantes.
In this work we investigate some extensions of the concept of absolutely summing operators, generalize some known results and provide partial answers to some open questions. For the class of absolutely (p; q; r)-summing mappings we obtain some inclusion and coincidence results and show that the ideal of absolutely (p; q; r)-summing polynomials is not coherent, according to the notion of coherent ideals due to D. Carando, V. Dimant and S. Muro. In order to bypass this deficiency, we introduce the concept of multiple (p; q; r)-summing multilinear and polynomial operators and show that, with this new approach, the ideal of multiple (p; q; r)-summing polynomials is coherent and compatible with the ideal of absolutely (p; q; r)-summing operators.
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14

Tuesta, Napoleon Caro. "Ideais de anéis de operadores diferenciais." Universidade de São Paulo, 2011. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-31082011-110130/.

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Em [12] J.T. Stafford demonstrou que todo ideal à esquerda ou à direita da álgebra de Weyl \'A IND. n\' (K) = K \'[ \'x IND. 1\', ...,\'x IND. n\' ] \' partial IND. 1\', ... \'partial IND. n\' (K um corpo de característica zero) é gerado por dois elementos. Consideremos o anel \'D IND. n\' := K [[\'x IND.1\', ...\'x IND. n\']] de operadores diferenciais sobre o anel de séries de potências formais K[[\'x IND. 1\';...\' xI ND. n\']]. Uma pergunta natural é se todo ideal à esquerda ou à direita de\' D IND. n\'(K) pode ser gerado por dois elementos. Neste trabalho provaremos que todo ideal à esquerda ou à direita do anel \'E IND. n\'(K) := K((\'x IND. 1\' ... \'x IND. n\'))(\' partial IND. 1, ...\'partial IND. n\') de operadores diferenciais sobre o corpo das séries de Laurent K((\'x IND. 1\', ...\'x IND. n\')) é gerado por dois elementos. Nós provaremos também que todo ideal à esquerda ou à direita do anel \'S IND. n -1\'(K) := K((\'x IND. 1\', ...\'X ind. n - 1\"))[[\'x IND. n\']](\' partial IND. 1, ...\'partial IND. n\') é gerado por dois elementos e como corolário obtemos uma demonstração que todo ideal à esquerda ou à direita do anel \'D IND. 1\'(K) é gerado por dois elementos. Isto está de acordo com a conjectura que diz que todo ideal à esquerda ou à direita de um anel (não comutativo) Noetheriano simples é gerado por dois elementos
In [12] J.T. Stafford proved that every left or right ideal of the Weyl algebra \'A IND. n\'(K) = K[\'x IND. 1\', ...\'x IND. n\'](\' partial IND. 1, ...\'partial IND. n\')(K a field of characteristic zero) is generated by two elements. Consider the ring \'D IND. n\' := K[[\'x IND. 1\', ...\'x IND.n\']](\'partial IND. 1\", ...\'partial IND. n) of differential operators over the ring of formal power series K[[\'x IND. 1\', ... \'x IND. n\']]: A natural question is that if every left or right ideal of \'D IND. n\'(K) can be generated by two elements. In this work we will prove that every left or right ideal of the ring \'E IND. n\' (K) := K((\'x IND. 1\', ... \'x IND. n\'))(\'partial IND. 1,...\'partial IND. n\') of differential operators over the field of formal Laurent series K((\'x IND. 1\', ...\'x IND. n\'))) is generated by two elements. We will prove also that every left or right ideal of the ring \'S IND. n -1\"(K) := K((\'x IND. 1\', ...\'x IND. n\'-1\'))[[\'x IND. n]](\'paertial IND. 1, ...\'partial IND. n\') is generated by two elements and as a corollary we obtain a proof of that every left or right ideal of the ring \'D IND. 1\'(K) is generated by two elements. This is in accordance with the conjecture that says that in a (noncommutative) Noetherian simple ring, every left or right ideal is generated by two elements
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15

Connon, Emma. "Generalizing Fröberg's Theorem on Ideals with Linear Resolutions." 2013. http://hdl.handle.net/10222/38565.

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In 1990, Fröberg presented a combinatorial classification of the quadratic square-free monomial ideals with linear resolutions. He showed that the edge ideal of a graph has a linear resolution if and only if the complement of the graph is chordal. Since then, a generalization of Fröberg's theorem to higher dimensions has been sought in order to classify all square-free monomial ideals with linear resolutions. Such a characterization would also give a description of all square-free monomial ideals which are Cohen-Macaulay. In this thesis we explore one method of extending Fröberg's result. We generalize the idea of a chordal graph to simplicial complexes and use simplicial homology as a bridge between this combinatorial notion and the algebraic concept of a linear resolution. We are able to give a generalization of one direction of Fröberg's theorem and, in investigating the converse direction, find a necessary and sufficient combinatorial condition for a square-free monomial ideal to have a linear resolution over fields of characteristic 2.
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16

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 technique lifts idempotent from the factor ring with the help of CNC system of ideals, which is a generalization of a well-known technique with nilpotent ideals, and it is here extended to group rings formed by non-abelian group and noncommutative ring. iii
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Nguyen, Thi Van Anh. "On Partial Regularities and Monomial Preorders." Doctoral thesis, 2018. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2018062823.

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My PhD-project has two main research directions. The first direction is on partial regularities which we define as refinements of the Castelnuovo-Mumford regularity. Main results are: relationship of partial regularities and related invariants, like the a-invariants or the Castelnuovo-Mumford regularity of the syzygy modules; algebraic properties of partial regularities via a filter-regular sequence or a short exact sequence; generalizing a well-known result for the Castelnuovo-Mumford regularity to the case of partial regularities of stable and squarefree stable monomial ideals; finally extending an upper bound proven by Caviglia-Sbarra to partial regularities. The second direction of my project is to develop a theory on monomial preorders. Many interesting statements from the classical theory of monomial orders generalize to monomial preorders. Main results are: a characterization of monomial preorders by real matrices, which extends a result of Robbiano on monomial orders; secondly, leading term ideals with respect to monomial preorders can be studied via flat deformations of the given ideal; finally, comparing invariants of the given ideal and the leading term ideal with respect to a monomial preorder.
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