Le « père de l'histoire whig » Thomas Babington Macaulay a été dès son vivant, et après sa mort, traduit dans nombre de pays, en Europe (Allemagne, France, Pays-Bas), comme hors des frontières européennes (Mexique). Incarnant à partir de la fin du XIXe siècle une histoire libérale progressiste et surtout non scientifique, attaquée par les historiens « professionnels », il n'en demeure pas moins très présent dans les manuels scolaires et universitaires jusqu'après la Seconde Guerre mondiale voire jusque dans les discours politiques contemporains. En 1931, puis en 1944, Herbert Butterfield tente de définir son interprétation de l'histoire. Ce dernier veut démontrer comment action politique et vision de l'histoire whigs incarnent un modèle, pragmatique, réformiste, à l'antithèse du modèle révolutionnaire français, qui explique l'exceptionnelle stabilité politique anglaise, britannique voire impériale du Royaume-Uni, depuis la Glorieuse Révolution. Dès lors les successeurs de Butterfield, en premier lieu J. G. A. Pocock et John Burrow, éclairent cette tradition libérale whig, devenue nationale, bientôt synonyme d'interprétation burkéenne de l'histoire. Pourtant, en s'appuyant sur le dialogue entre libéraux britanniques (whigs comme Millar, Mackintosh, utilitaristes comme les Mill, père et fils) et libéraux français (comme Constant, Guizot et Tocqueville), illustrant par ailleurs les riches échanges entre Royaume-Uni et France au XIXe siècle – avant que l’oeuvre de Macaulay ne soit que très épisodiquement traduite et commentée au XXe siècle en France –, et sur une étude minutieuse des écrits de Macaulay portant sur la Révolution française, cette thèse entend démontrer qu'au - delà de la division politique du parti whig lors de la période révolutionnaire, l'histoire whig de Macaulay incarne une pensée politique, une interprétation des révolutions anglaises et françaises et une philosophie libérale de l'histoire nouvelles rompant avec Hume et avec Burke. En mettant au coeur de l'histoire l'émancipation politique et religieuse des individus, Macaulay défend la démocratisation et la laïcisation des sociétés et illustre une histoire libérale post-Révolutionnaire, un nouveau paradigme whig, qui ne peuvent être qualifiés de conservateurs ni de contre-Révolutionnaires. / The "father of Whig History", Thomas Babington Macaulay, was, during his lifetime and after his death,translated in numerous European countries ( Germany, France, The Netherlands ) as well as outside Europe(Mexico). Embodying, from the end of the nineteenth century, a liberal, progressive and especially nonscientifichistory, denounced by "professional " historians, he remained no less highly present in school anduniversity textbooks up to the Second World War, and even in contemporary and current political speeches.In 1931, and then in 1944, Herbert Butterfield attempted to define his interprétation of history and sought todemonstrate how political action and historical vision embody a pragmatic and reformist model, theantithesis of the French revolutionary model, which explains the exceptional English, British, even imperial,political stability of Great Britain since the Glorious Revolution. Since then, Butterfield's successors, andfirst among them, J. G. A. Pocock and John Burrow, have been shedding light on this liberal, becomenational, whig tradition, soon to be synonymous with the Burkean interpretation of history. However, basedon the dialogue between British liberals ( Whigs such as Millar and Mackintosh, Utilitarians such as theMills, father and son ), and French liberals ( such as Constant, Guizot and Tocqueville), while illustrating inother respects the fruitful exchange between Great Britain and France during the nineteenth century - beforeMacaulay's work was only very episodically translated and commented on in the twentieth century in France- and on a thorough exploration of Macaulay's work on the French Revolution, this study intends todemonstate that beyond the political division of the Whig party during the revolutionary period, Macaulay'sWhig history sanctions a new line of political thought, a new interprétation of the English and FrenchRévolutions and liberal philosophy of history, breaking with Hume and Burke. By placing the political andreligious emancipation of individuals at the heart of history, Macaulay defended the democratization and thesecularization of society and illustrated a post-Revolutionary liberal history, a new Whig paradigm, thatcannot be called conservative nor counter- revolutionary.

Discusses the contrasts apparent in the Victorian era British writers Carlyle and Macaulay with reference to history, biography, and literary criticism.

Submitted by Fabrício Rissão Mattos (farissao@gmail.com) on 2018-10-02T19:09:41Z No. of bitstreams: 1 Dissertação pronta.pdf: 1097649 bytes, checksum: 443e2ed81081a595f708a0c46d351f7c (MD5) / Approved for entry into archive by Elza Mitiko Sato null (elzasato@ibilce.unesp.br) on 2018-10-02T19:18:24Z (GMT) No. of bitstreams: 1 mattos_fr_me_sjrp.pdf: 1097649 bytes, checksum: 443e2ed81081a595f708a0c46d351f7c (MD5) / Made available in DSpace on 2018-10-02T19:18:24Z (GMT). No. of bitstreams: 1 mattos_fr_me_sjrp.pdf: 1097649 bytes, checksum: 443e2ed81081a595f708a0c46d351f7c (MD5) Previous issue date: 2018-08-30 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Neste trabalho definimos o polinômio de Hilbert-Samuel cuja descrição desse polinômio aparecem o foco principal do nosso estudo os coeficientes normalizados de Hilbert. A princípio vamos estudar, sobre determinadas condições iniciais, os sinais dos coeficientes que denotaremos por e0(q,M), e1(q,M) e e2(q,M). Teremos ao final desse trabalho, em formato de comentário, uma condição necessária e suficiente para que todos os coeficientes normalizados de Hilbert sejam nulos. / In this work we define the Hilbert-Samuel polynomial whose description of this polynomial appear the main focus of our study the normalized Hilbert coefficients. At first, we will study, on certain initial conditions, the signals of the coefficients that we denoteby e1(q,M) e e2(q,M). Wewillhaveattheendofthiswork,inacommentformat, a necessary and sufficient condition so that all normalized Hilbert coefficients are null. / 132997/2016-9

Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-21T14:11:17Z No. of bitstreams: 1 arquivo total.pdf: 931330 bytes, checksum: 351b504f68153fb01d23f3fd1d96d2a0 (MD5) / Made available in DSpace on 2016-03-21T14:11:17Z (GMT). No. of bitstreams: 1 arquivo total.pdf: 931330 bytes, checksum: 351b504f68153fb01d23f3fd1d96d2a0 (MD5) Previous issue date: 2013-04-29 / In this work, after the introduction of some concepts of Commutative Algebra, for instance dimension, minimal number of generators, and multiplicity, we prove the existence of a very special class of modules over Cohen-Macaulay rings, the so-called Ulrich modules. It is known that, if M is a maximal Cohen-Macaulay module over such ring, then (M) e(M). Our goal in this study is to prove the main cases where the equality (M) e(M) holds. / Neste trabalho, após introduzirmos alguns conceitos de Álgebra Comutativa, como dimensão, número mínimo de geradores, e multiplicidade, provamos a existência de uma classe de módulos bastante especial sobre anéis Cohen-Macaulay, os chamados módulos de Ulrich. É sabido que, se M é um A-módulo Cohen-Macaulay maximal sobre um tal anel, então (M) e(M). O objetivo do nosso estudo é demonstrar os principais casos em que vale (M) = e(M).

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The purpose of this dissertation is to introduce the notion of local cohomology as well as some of its applications. Initially, we performed a brief review on the main homological tools used in this work, such as: homology of a complex, isomorphism of complexes, injective resolutions, derived functors, etc. Next, we detail properties of the injective modules in the context of Noetherian rings. Finally, we present di erent ways of de ning local cohomology and we show how this notion is used to investigate the arithmetical rank of an ideal. / O objetivo dessa dissertação é introduzir a noção de cohomologia local bem como algumas de suas aplicações. Inicialmente, realizamos um breve apanhado sobre as principais noções homológicas utilizadas no trabalho, tais como: homologia de um complexo, isomorfismo de complexos, resoluções injetivas, funtores derivados, etc. Em seguida, detalhamos propriedades dos módulos injetivos no contexto dos anéis Noetherianos. Finalmente, apresentamos formas variadas de definir cohomologia local e mostramos como essa noção é utilizada para investigar o posto aritmético de um ideal.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / David Mumford introduced the concept of regularity of a coherent beam into the projective space in terms of local cohomology, generalizing a classic argument of Castelnuovo. In this dissertation under view of commutative algebra, we will introduce the concept of regularity of finitely generated graduated modules on the ring of polynomials. First, we perform a preliminary study on dimension theory and especially on Hilbert’s function. We also studied the basics of Cohen- Macaulay modules, properties of Betti’s graduated numbers, and the local cohomology functors. In the main chapter, we define the regularity of Castelnuovo-Mumford using the free resolution shifts. Soon after, we show that the definition of regularity can be given in terms of local cohomology, with emphasis on the cases of Artinian and Cohen-Macaulay modules. / David Mumford introduziu o conceito de regularidade de um feixe coerente no espac¸o projetivo em termos de cohomologia local, generalizando um argumento cl´assico de Castelnuovo. Nessa dissertac¸ ˜ao sob a vis˜ao da ´algebra comutativa, introduziremos o conceito de regularidade de m´odulos graduados finitamente gerados sobre o anel de polinˆomios. Primeiramente realizamos um estudo preliminar sobre teoria da dimens˜ao e em especial sobre a func¸ ˜ao de Hilbert. Tamb´em estudamos noc¸ ˜oes b´asicas em m´odulos Cohen-Macaulay, propriedades dos n´umeros graduados de Betti e dos funtores de cohomologia local. No cap´ıtulo principal, definimos a regularidade de Castelnuovo-Mumford utilizando os shifts de resoluc¸ ˜oes livres. Logo ap´os, mostramos que a definic¸ ˜ao de regularidade pode ser dada em termos de cohomologia local, dando ˆenfase aos casos de m´odulos Artinianos e Cohen-Macaulay. / São Cristóvão, SE

La théorie des champs de vecteurs logarithmiques et des formes différentielles logarithmiques d’une hypersurface singulière réduite est développée par K.Saito. Ces notions apparaissent dans l’étude de la connexion de Gauss-Manin de certaines familles de singularités et de leur déploiement semi-universel.Lorsque le module des champs de vecteurs logarithmiques est libre, l’hypersurface est appelée diviseur libre. A.G. Aleksandrov et A. Tsikh généralisent les notions de formes différentielles logarithmiques et de résidus logarithmiques aux intersections complètes et aux espaces de Cohen-Macaulay réduits.Nous étudions dans ce travail les formes différentielles logarithmiques d’un espace singulier réduit de codimension quelconque plongé dans une variété lisse, et nous développons une notion de singularités libres qui étend la notion de diviseurs libres. Les résidus des formes différentielles logarithmiques d’une hypersurface ainsi que leur généralisation aux espaces de codimension supérieure interviennent de façon cruciale dans ce travail de thèse. Notre premier objectif est de donner des caractérisations de la liberté pour les intersections complètes et les espaces de Cohen-Macaulay qui généralisent le cas des hypersurfaces. Nous accordons ensuite une attention particulière à une famille de singularités libres, à savoir les courbes, pour lesquelles nous décrivons le module des résidus logarithmiques en termes de multi-valuations. / The theory of logarithmic vector fields and logarithmic differential forms along a reduced singular hypersurface is developed by K. Saito. These notions appear in the study of the Gauss-Manin connection of some families of singularities and their semi-universal unfolding. If the module of logarithmic vector fields is free, the hypersurface is called a free divisor. A.G. Aleksandrov and A. Tsikh generalize the notions of logarithmic differential forms and logarithmic residues to reduced complete intersections and Cohen-Macaulay spaces. In this work, we study the logarithmic differential forms of a reduced singular space of any codimension embedded in a smooth manifold, and we develop a notion of free singularity which extend the notion of free divisor. The residues of logarithmic differential forms as well as theirgeneralization to higher codimension spaces are crucial in this thesis. Our first purpose is to give characterizations of freeness for complete intersections and Cohen-Macaulay spaces which generalize the case of hypersurfaces. We then give a particular attention to a family of free singularities, namely the curves, for which we describe the module of logarithmic residues thanks to their set of values.

<div>In the first part of this thesis, we study Rees algebras of modules. We investigate their Cohen-Macaulay property and their defining ideal, using <i>generic Bourbaki ideals</i>. These were introduced by Simis, Ulrich and Vasconcelos in [65], in order to characterize the Cohen-Macaulayness of Rees algebras of modules. Thanks to this technique, the problem is reduced to the case of Rees algebras of ideals. Our main results are the following.</div><div><br></div><div><div>In Chapters 3 and 4 we consider a finite module <i>E</i> over a Gorenstein local ring <i>R</i>. In Theorem 3.2.4 and Theorem 4.3.2, we give sufficient conditions for <i>E</i> to be of linear type, while Theorem 4.2.4 provides a sufficient condition for the Rees algebra <i>R(E)</i> of <i>E</i> to be Cohen-Macaulay. These results rely on properties of the residual intersections of a generic Bourbaki ideal <i>I</i> of<i> E</i>, and generalize previous work of Lin (see [46, 3.1 and 3.4]). In the case when <i>E</i> is an ideal, Theorem 4.2.4 had been previously proved independently by Johnson and Ulrich (see [39, 3.1]) and Goto, Nakamura and Nishida (see [20, 1.1 and 6.3]).</div></div><div><br></div><div><div>In Chapter 5, we consider a finite module <i>E</i> of projective dimension one over <i>k</i>[X₁, . . . , X_n]. Our main result, Theorem 5.2.6, describes the defining ideal of <i>R(E)</i>, under the assumption that the presentation matrix φ of <i>E</i> is <i>almost linear</i>, i.e. the entries of all but one column of φ are linear. This theorem extends to modules a known result of Boswell and Mukundan on the Rees algebra of almost linearly presented perfect ideals of height 2 (see [5, 5.3 and 5.7]).</div></div><div><br></div><div><div>The second part of this thesis studies the Cohen-Macaulay property of the special fiber ring<i> F(E)</i> of a module <i>E</i>. In Theorem 6.2.14, we prove that the generic Bourbaki ideals of Simis, Ulrich and Vasconcelos allow to reduce the problem to the case of fiber cones of ideals, similarly as for Rees algebras. We then provide sufficient conditions for <i>F(E)</i> to be Cohen-Macaulay. Our Theorems 6.2.15, 6.1.3 and 6.2.18 are module versions of results proved for the fiber cone of an ideal by Corso, Ghezzi, Polini and Ulrich (see [10, 3.1] and [10, 3.4]) and by Monta˜no (see [47, 4.8]), respectively.</div></div><div><br></div>

Thesis (M. Phil.)--University of Hong Kong, 2005. / Also available in print.

Polyominoes are two-dimensional objects obtained by joining edge by edge squares of same size. Originally, polyominoes appeared in mathematical recreations, but it turned out that they have applications in various fields, for example, theoretical physics and bio-informatics. Among the most popular topics in combinatorics related to polyominoes one finds enumerating polyominoes of given size, including the asymptotic growth of the numbers of polyominoes, tiling problems, and reconstruction of polyominoes. Recently Qureshi introduced a binomial ideal induced by the geometry of a given polyomino, called polyomino ideal, and its related algebra. From that moment different authors studied algebraic properties and invariants related to this ideal, such as primality, Gröbner bases, Gorensteinnes and Castelnuovo-Mumford regularity. In this thesis, we provide an overview on the results that we obtained about polyomino ideals and its related algebra. In the first part of the thesis, we discuss questions about the primality and the Gröbner bases of the polyomino ideal. In the second part of the thesis, we talk over the Castelnuovo-Mumford regularity, Hilbert series, and Gorensteinnes of the polyomino ideal and its coordinate ring.