Cette thèse présente des calculs d’algèbre homologique dans la catégorie des modules instables. Dans le premier chapitre, on rappelle des généralités sur cette catégorie, parmi elles le théorème de la caractérisation de la filtration de Krull grâce au foncteur de Lannes. En utilisant la théorie des représentations, Schwartz a démontré ce théorème dans les années 90s. Au cours du chapitre, on donne une preuve élémentaire de ce théorème. Une méthode efficace pour construire des résolutions à partir des suites exactes dans cette catégorie y est introduite ainsi. On l’appelle pseudo-hyper résolution. La catégorie des foncteurs polynomiaux stricts homogènes de degré fini a été reliée avec la catégorie des modules instables d’après les travaux de Hai en 2010. Le foncteur connectant ces deux catégories est nommé d’après lui. On montre dans le deuxième chapitre que ce foncteur est pleinement fidèle, permettant de considérer la catégorie des foncteurs polynomiaux stricts homogènes de degré fini comme une sous-catégorie pleine de la catégorie des modules instables. Le chapitre 3 est consacré pour étudier les résolutions injectives minimales des cohomologies de sphères. On montre que le morphisme à la Bockstein permet de déterminer une grande partie de ces résolutions. Dans le dernier chapitre, on étudie l’action de la torsion de Frobenius sur les groupes d’extensions. Ceci amène à étudier la résolution injective minimale du module F(1), étant générateur projectif monogène engendré par un élément de degré 1. De l’information partielle de la partie nilpotente de cette résolution est donnée à la fin du chapitre. / The aim of this work is to study injective resolutions of certain objects in the category U of unstable modules. More precisely, we concentrate on the minimal injective resolution of the module F(1) as well as ones of the cohomology of spheres ΣnF2.For that purpose, the pseudo-hyper resolution is introduced, allowing to construct an explicit resolution of an unstable module from an acyclic sequence admitting this module as its first homology. This construction and the hyper resolution do look alike but are not identical. In our situation, we consider the sequence without splitting it into short exact sequences to avoid unnecessary concerns about the differentials. Placing the resolutions of each term in the sequence together, we obtain a fake double complex. Fortunately, the injectivity of modules in this double complex allow us to insert enough differentials that make the total sequence a complex. This complex is indeed the resolution for the considered module. To deal with the particular cases of ΣnF2, the pseudo-hyper resolution wil be translated into the algorithm BG. Together with this procedure, the Bockstein sequence gives a simple description on a large part of the minimal injective resolution of ΣnF2.The minimal injective resolution of F(1) is too much to deal with. Few results on this matter have been known. Luckily the nilpotent part of this resolution is quite accessible. Using the computations on the derived functors `∗(F(1)) and the groupes Ext we first show that this part is periodic and then give a simple description for several terms. These are crucial to show that the natural map ExtrU (ΦnF(1),ΦnF(1)) → ExtrU Φn+1F(1),Φn+1F(1) is injective in many cases.The work is also decorated with a new elemenatary proof on the characterization of the Krull filtration and a fully faithful embedding from the category Pd to the category U.

In the first chapter we give an outline of classical KRULL rings as in SAMUEL (1964), BOURBAKI (1965) and FOSSUM (1973). In the second chapter we introduce two notions important to our treatment of KRULL theory. The first is injective modules and.the second torsion theories. We then look at injective modules over Noetherian rings as in MATLIS [1958] and then over KRULL rings as in BECK [1971]. We show that for a KRULL ring there is a torsion theory (N,M) where N is the pseudo-zero modules and M the set of N-torsion-free (BECK calls these co-divisorial) modules. From LAMBEK [1971] there is a full abelian sub category C, namely the category of N-torsion-free, N-divisible modules, with exact reflector. We show in C (I) every direct sum of injective modules is injective and (II) C has global dimension at most one. It is these two properties that we exploit in the third chapter to give another characterization of KRULL rings. Then we generalize this to rings with zero-divisors and find that (i) R has to be reduced (ii) the ring is KRULL if and only if it is a finite product of fields and KRULL domains (iii) the injective envelope of the ring is semi-simple artinian. We then generalize the ideas to rings of higher dimension.

Groups of divisibility have played an important role in commutative algebra for many years. In 1932 Wolfgang Krull showed in [12] that every linearly ordered Abelian group can be realized as the group of divisibility of a valuation domain. Since then it has also been proven that every lattice-ordered Abelian group can be recognized as the group of divisibility of a Bezont domain. Knowing these two facts allows us to use groups of divisibility to find examples of rings with highly exotic properties. For instance, we use them here to find examples of rings which admit elements that factor uniquely as the product of uncountably many primes. In addition to allowing us to create examples, groups of divisibility can he used to characterize some of the most important rings most commonly encountered in factorization theory, including valuation domains, UFD's, GCD domains, and antimatter domains. We present some of these characterizations here in addition to using them to create many examples of our own, including examples of rings which admit chains of prime ideals in which there are uncountably many primes in the chain. Moreover, we use groups of divisibility to prove that every fragmented domain must have infinite Krull dimension.

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A presente dissertação consiste na comparação dos romances Memórias póstumas de Brás Cubas e Confissões do impostor Felix Krull. Procuramos analisar os aspectos que os aproximam, apesar do afastamento temporal e cultural entre eles existente, partindo dos elementos que imitam o texto autobiográfico e suas respectivas implicações. Tanto as vidas representadas nos dois romances afastam-se do que se entende por uma biografia normal, como também a particular tarefa autobiográfica realizada por Felix e Brás foge do padrão de confissões e de memórias. A confiabilidade dos narradores pode ser ainda questionada, haja vista suas singulares condições enquanto narradores: um, impostor, e outro, defunto. Esta dissertação é composta por seis partes, nas quais se discutirão os seguintes aspectos: introdução à análise comparativa, os romances e os narradores, a intertextualidade inserida na forma e na temática, o decurso de vida de Brás e Felix, suas condições como autobiógrafos e o papel do leitor. No que diz respeito a este último aspecto, podemos afirmar que como o romance em geral, Memórias póstumas e Confissões, que simulam o relato autobiográfico, se preocupam com a função do público. Nos dois livros em questão, essa preocupação reflete-se nos papéis do leitor inseridos nas narrativas. Nossa dissertação ocupar-se-á desse aspecto como último e com particular atenção, visando analisar as reflexões metanarrativas realizadas pelos narradores diante de seus respectivos leitores no horizonte da autobiografia ficcional. / The following degree thesis consists in comparing the novels Memórias póstumas de Brás Cubas and Confissões do impostor Felix Krull. We attempted to analyse the aspects, which approach them, despite of the temporal and cultural distance between them, initiating from the elements, which imitate the autobiographical text and its respective implications. The lives represented in both novels diverge from what usually can be understood as a normal biography. In a similar way the autobiographical function assumed by Felix and Brás diverges from the ideal standard of the confession and the autobiographical memory. The reliability of the narrators can be also questioned if we considerate their singular conditions as narrators: one, as impostor, the other, as a dead person. This thesis is composed of six parts, in that we will discuss the following aspects: an introduction to the comparative analysis, the novels and their narrators, the intertextuality introduced in the form and in the subject, Brás and Felix life events, their condition as autobiographers and the readers role. Like the novels in general, Memórias póstumas e Confissões, that simulate the autobiographical narrative, attend to the role of the attendance. In both analised books this concern is reflected on the the readers inserted in the narratives. This dissertation handles this aspect lastly, trying to analyse the Felix and Brás metanarrative considerations according to their respective readers in the horizon of the fictional autobiography.

Fundação de Apoio a Pesquisa e à Inovação Tecnológica do Estado de Sergipe - FAPITEC/SE / The Rees algebra of an ideal is an algebraic construction that takes place in commutative algebra and algebraic geometry. Currently, the study of arithmetic and homological properties of this object is cause for diverse research in commutative algebra. Our main goal in this work is to address aspects such as dimension and defining equations of the Rees algebra and other algebras that relate to it. / A álgebra de Rees de um ideal é uma construção algébrica que ocupa lugar de destaque na álgebra comutativa e na geometria algébrica. Atualmente, o estudo de propriedades aritméticas e homológicas desse objeto é motivo de diversas pesquisas em álgebra comutativa. Nosso principal objetivo nesse trabalho é tratar de aspectos como dimensão e equações de definição da álgebra de Rees e de outras álgebras que relacionam-se com ela.

A presente dissertação consiste na comparação dos romances Memórias póstumas de Brás Cubas e Confissões do impostor Felix Krull. Procuramos analisar os aspectos que os aproximam, apesar do afastamento temporal e cultural entre eles existente, partindo dos elementos que imitam o texto autobiográfico e suas respectivas implicações. Tanto as vidas representadas nos dois romances afastam-se do que se entende por uma biografia normal, como também a particular tarefa autobiográfica realizada por Felix e Brás foge do padrão de confissões e de memórias. A confiabilidade dos narradores pode ser ainda questionada, haja vista suas singulares condições enquanto narradores: um, impostor, e outro, defunto. Esta dissertação é composta por seis partes, nas quais se discutirão os seguintes aspectos: introdução à análise comparativa, os romances e os narradores, a intertextualidade inserida na forma e na temática, o decurso de vida de Brás e Felix, suas condições como autobiógrafos e o papel do leitor. No que diz respeito a este último aspecto, podemos afirmar que como o romance em geral, Memórias póstumas e Confissões, que simulam o relato autobiográfico, se preocupam com a função do público. Nos dois livros em questão, essa preocupação reflete-se nos papéis do leitor inseridos nas narrativas. Nossa dissertação ocupar-se-á desse aspecto como último e com particular atenção, visando analisar as reflexões metanarrativas realizadas pelos narradores diante de seus respectivos leitores no horizonte da autobiografia ficcional. / The following degree thesis consists in comparing the novels Memórias póstumas de Brás Cubas and Confissões do impostor Felix Krull. We attempted to analyse the aspects, which approach them, despite of the temporal and cultural distance between them, initiating from the elements, which imitate the autobiographical text and its respective implications. The lives represented in both novels diverge from what usually can be understood as a normal biography. In a similar way the autobiographical function assumed by Felix and Brás diverges from the ideal standard of the confession and the autobiographical memory. The reliability of the narrators can be also questioned if we considerate their singular conditions as narrators: one, as impostor, the other, as a dead person. This thesis is composed of six parts, in that we will discuss the following aspects: an introduction to the comparative analysis, the novels and their narrators, the intertextuality introduced in the form and in the subject, Brás and Felix life events, their condition as autobiographers and the readers role. Like the novels in general, Memórias póstumas e Confissões, that simulate the autobiographical narrative, attend to the role of the attendance. In both analised books this concern is reflected on the the readers inserted in the narratives. This dissertation handles this aspect lastly, trying to analyse the Felix and Brás metanarrative considerations according to their respective readers in the horizon of the fictional autobiography.

The elasticity of a Krull domain R is equivalent to the elasticity of the block monoid B(G,S), where G is the divisor class group of R and S is the set of elements of G containing a height-one prime ideal of R. Therefore the elasticity of R can by studied using the divisor class group. In this dissertation, we will study infinite divisor class groups to determine the elasticity of the associated Krull domain. The results will focus on the divisor class groups Z, Z(p infinity), Q, and general infinite groups. For the groups Z and Z(p infinity), it has been determined which distributions of the height-one prime ideals will make R a half-factorial domain (HFD). For the group Q, certain distributions of height-one prime ideals are proven to make R an HFD. Finally, the last chapter studies general infinite groups and groups involving direct sums with Z. If certain conditions are met, then the elasticity of these divisor class groups is the same as the elasticity of simpler divisor class groups.

Le but de ce travail est d'étudier la structure globale de la catégorie de foncteurs F entre espaces vectoriels sur F_2, notamment la conjecture artinienne, qui équivaut au caractère localement noethérien de cette catégorie. Nous démontrons que le produit tensoriel entre un foncteur fini et le foncteur projectif standard P tenseur 2 est noethérien.<br /> Nous introduisons à cet effet d'autres catégories de foncteurs, nommées catégories de foncteurs en grassmanniennes. Elles permettent d'énoncer une forme très forte de la conjecture artinienne, décrivant la filtration de Krull de la catégorie F. Notre théorème de simplicité généralisé établi une version faible de cette conjecture. Il permet de démontrer le résultat précédent sur la structure de P tenseur 2 tenseur F (avec F fini), que nous avons également obtenu par l'usage conjoint de foncteurs hom internes et de considérations issues de la théorie des représentations modulaires.<br /> Nous décrivons la riche structure algébrique des catégories de foncteurs en grassmanniennes, équivalentes à des catégories de comodules dans F. Notre théorème d'annulation cohomologique fondamental généralise un grand nombre de résultats antérieurs en cohomologie des foncteurs. Il permet également de généraliser une étape essentielle de la démonstration de Suslin de l'isomorphisme entre K-théorie stable et homologie de Mac Lane pour des systèmes de coefficients polynomiaux.

Made available in DSpace on 2016-03-12T02:03:58Z (GMT). No. of bitstreams: 1 000477584-Texto+Completo-0.pdf: 1092322 bytes, checksum: ac82eb1aeaaddb2a96a668740314f72f (MD5) Previous issue date: 2016 / This is an essay of aesthetic expression written for doctoral thesis purposes, and it explores the work Confessions of Felix Krull, from Thomas Mann. In order to understand this particular work from Thomas Mann, the author also permeates other works by the german writer. The analysis has its central philosophical basis on the Aesthetic theory of Theodor Adorno. The main concepts worked in this writing are mimesis, subjectivity and the idea of natural history. Another concepts such as essay, constellation, montage and model are also mobilized to understand the object of the thesis. The objective is to comprehend a particular structure of the hegemonic language in the western world, taking into consideration this singular work from Thomas Mann, which he had started writing in 1910 and finally published in 1954. The work was divided into three axes of analysis: one on the expression and language of the Confessions, the other on the narrator subject and on the impostor who confesses, and, finally, the analysis of a scene where the author sought uniqueness as critical and dialectical expression. / Trata-se de um ensaio de expressão estética, escrito para fins de tese de doutorado, que versa sobre a obra Confissões do impostor Felix Krull, de Thomas Mann. Para a compreensão dessa obra específica o autor perpassa também por outras obras do escritor alemão. A análise tem como base filosófica central a Teoria estética de Theodor Adorno. Os principais conceitos abordados nesse trabalho são a mímesis, a subjetividade e a ideia de história natural. Outros conceitos como ensaio, constelação, montagem e modelo também são mobilizados para a compreensão do objeto de tese. Objetiva-se compreender uma determinada estrutura de linguagem hegemônica no mundo ocidental, a partir desta obra singular, cujo início foi escrito em 1910 e publicada finalmente no ano de 1954. O trabalho foi estruturado em três eixos de análise: um sobre a expressão e a linguagem das Confissões, outro sobre o sujeito narrador e impostor que confessa e, por fim, a análise de uma cena, buscando a singularidade como expressão crítica e dialética.