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    https://sophisticatedspectra.com/article/drosia-serenity-a-modern-oasis-in-the-heart-of-larnaca.2521391.html

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    The Valuative Tree

    Posted By: AvaxGenius
    The Valuative Tree

    The Valuative Tree by Charles Favre , Mattias Jonsson
    English | PDF (True) | 2004 | 251 Pages | ISBN : 3540229841 | 3.7 MB

    This volume is devoted to a beautiful object, called the valuative tree and designed as a powerful tool for the study of singularities in two complex dimensions. Its intricate yet manageable structure can be analyzed by both algebraic and geometric means. Many types of singularities, including those of curves, ideals, and plurisubharmonic functions, can be encoded in terms of positive measures on the valuative tree. The construction of these measures uses a natural tree Laplace operator of independent interest.

    Almost Ring Theory

    Posted By: AvaxGenius
    Almost Ring Theory

    Almost Ring Theory by Ofer Gabber , Lorenzo Ramero
    English | PDF (True) | 2003 | 314 Pages | ISBN : 3540405941 | 4 MB

    This book develops thorough and complete foundations for the method of almost etale extensions, which is at the basis of Faltings' approach to p-adic Hodge theory. The central notion is that of an "almost ring". Almost rings are the commutative unitary monoids in a tensor category obtained as a quotient V-Mod/S of the category V-Mod of modules over a fixed ring V; the subcategory S consists of all modules annihilated by a fixed ideal m of V, satisfying certain natural conditions.

    Galois Theory of Linear Differential Equations

    Posted By: AvaxGenius
    Galois Theory of Linear Differential Equations

    Galois Theory of Linear Differential Equations by Marius Put , Michael F. Singer
    English | PDF (True) | 2003 | 446 Pages | ISBN : 3540442286 | 3.9 MB

    Linear differential equations form the central topic of this volume, Galois theory being the unifying theme.
    A large number of aspects are presented: algebraic theory especially differential Galois theory, formal theory, classification, algorithms to decide solvability in finite terms, monodromy and Hilbert's 21st problem, asymptotics and summability, the inverse problem and linear differential equations in positive characteristic. The appendices aim to help the reader with concepts used, from algebraic geometry, linear algebraic groups, sheaves, and tannakian categories that are used.

    Rational Homotopy Theory and Differential Forms

    Posted By: AvaxGenius
    Rational Homotopy Theory and Differential Forms

    Rational Homotopy Theory and Differential Forms by Phillip Griffiths , John Morgan
    English | PDF (True) | 2013 | 228 Pages | ISBN : 1461484677 | 1.7 MB

    This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham’s theorem on simplicial complexes. In addition, Sullivan’s results on computing the rational homotopy type from forms is presented.

    Introduction à la résolution des systèmes polynomiaux

    Posted By: AvaxGenius
    Introduction à la résolution des systèmes polynomiaux

    Introduction à la résolution des systèmes polynomiaux by Mohamed Elkadi , Bernard Mourrain
    Français | PDF | 2007 | 308 Pages | ISBN : 3540716467 | 2.1 MB

    Les équations polynomiales apparaissent dans de nombreux domaines, pour modéliser des contraintes géométriques, des relations entre des grandeurs physiques, ou encore des propriétés satisfaites par certaines inconnues. Cet ouvrage est une introduction aux méthodes algébriques permettant de résoudre ce type d'équations. Nous montrons comment la géométrie des variétés algébriques définies par ces équations, leur dimension, leur degré, ou leurs composantes peuvent se déduire des propriétés des algèbres quotients correspondantes. Nous abordons pour cela des méthodes de la géométrie algébrique effective, telles que les bases de Grobner, la résolution par valeurs et vecteurs propres, les résultants, les bezoutiens, la dualité, les algèbres de Gorenstein et les résidus algébriques. Ces méthodes sont accompagnées d'algorithmes, d'exemples et d'exercices, illustrant leurs applications.

    Algèbre commutative: Chapitres 8 et 9

    Posted By: AvaxGenius
    Algèbre commutative: Chapitres 8 et 9

    Algèbre commutative: Chapitres 8 et 9 by N. Bourbaki
    Français | PDF | 2006 | 204 Pages | ISBN : 3540339426 | 10.1 MB

    Les Éléments de mathématique de Nicolas Bourbaki ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements.

    Advances in Ring Theory

    Posted By: AvaxGenius
    Advances in Ring Theory

    Advances in Ring Theory by Dinh Huynh, Sergio R. López-Permouth
    English | PDF (True) | 2010 | 345 Pages | ISBN : 3034602855 | 2.6 MB

    This volume consists of refereed research and expository articles by both plenary and other speakers at the International Conference on Algebra and Applications held at Ohio University in June 2008, to honor S.K. Jain on his 70th birthday. The articles are on a wide variety of areas in classical ring theory and module theory, such as rings satisfying polynomial identities, rings of quotients, group rings, homological algebra, injectivity and its generalizations, etc. Included are also applications of ring theory to problems in coding theory and in linear algebra.

    Resolution of Curve and Surface Singularities in Characteristic Zero

    Posted By: AvaxGenius
    Resolution of Curve and Surface Singularities in Characteristic Zero

    Resolution of Curve and Surface Singularities in Characteristic Zero by K. Kiyek , J. L. Vicente
    English | PDF | 2004 | 506 Pages | ISBN : 1402020287 | 50.3 MB

    The Curves The Point of View of Max Noether Probably the oldest references to the problem of resolution of singularities are found in Max Noether's works on plane curves [cf. [148], [149]]. And probably the origin of the problem was to have a formula to compute the genus of a plane curve. The genus is the most useful birational invariant of a curve in classical projective geometry. It was long known that, for a plane curve of degree n having l m ordinary singular points with respective multiplicities ri, i E {1, . . . , m}, the genus p of the curve is given by the formula = (n - l)(n - 2) _ ~ "r. (r. _ 1) P 2 2 L. . ,. •• . Of course, the problem now arises: how to compute the genus of a plane curve having some non-ordinary singularities. This leads to the natural question: can we birationally transform any (singular) plane curve into another one having only ordinary singularities? The answer is positive. Let us give a flavor (without proofs) 2 on how Noether did it • To solve the problem, it is enough to consider a special kind of Cremona trans­ formations, namely quadratic transformations of the projective plane. Let ~ be a linear system of conics with three non-collinear base points r = {Ao, AI, A }, 2 and take a projective frame of the type {Ao, AI, A ; U}.

    Groups, Matrices, and Vector Spaces: A Group Theoretic Approach to Linear Algebra (Repost)

    Posted By: AvaxGenius
    Groups, Matrices, and Vector Spaces: A Group Theoretic Approach to Linear Algebra (Repost)

    Groups, Matrices, and Vector Spaces: A Group Theoretic Approach to Linear Algebra by James B. Carrell
    English | PDF | 2017 | 414 Pages | ISBN : 0387794271 | 4.3 MB

    This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group.

    Commutative Algebra: Noetherian and Non-Noetherian Perspectives

    Posted By: AvaxGenius
    Commutative Algebra: Noetherian and Non-Noetherian Perspectives

    Commutative Algebra: Noetherian and Non-Noetherian Perspectives by Marco Fontana, Salah-Eddine Kabbaj, Bruce Olberding, Irena Swanson
    English | PDF(True) | 2011 | 490 Pages | ISBN : 1441969896 | 4.5 MB

    Commutative algebra is a rapidly growing subject that is developing in many different directions. This volume presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutative algebra.

    The Use of Ultraproducts in Commutative Algebra (Repost)

    Posted By: AvaxGenius
    The Use of Ultraproducts in Commutative Algebra (Repost)

    The Use of Ultraproducts in Commutative Algebra by Hans Schoutens
    English | PDF | 2010 | 215 Pages | ISBN : 3642133673 | 2.6 MB

    In spite of some recent applications of ultraproducts in algebra, they remain largely unknown to commutative algebraists, in part because they do not preserve basic properties such as Noetherianity. This work wants to make a strong case against these prejudices. More precisely, it studies ultraproducts of Noetherian local rings from a purely algebraic perspective, as well as how they can be used to transfer results between the positive and zero characteristics, to derive uniform bounds, to define tight closure in characteristic zero, and to prove asymptotic versions of homological conjectures in mixed characteristic. Some of these results are obtained using variants called chromatic products, which are often even Noetherian. This book, neither assuming nor using any logical formalism, is intended for algebraists and geometers, in the hope of popularizing ultraproducts and their applications in algebra.

    Commutative Algebra: Volume II

    Posted By: AvaxGenius
    Commutative Algebra: Volume II

    Commutative Algebra: Volume II by Oscar Zariski , Pierre Samuel
    English | PDF | 1960 | 425 Pages | ISBN : 3662277530 | 41.9 MB

    This second volume of our treatise on commutative algebra deals largely with three basic topics, which go beyond the more or less classical material of volume I and are on the whole of a more advanced nature and a more recent vintage. These topics are: (a) valuation theory; (b) theory of polynomial and power series rings (including generalizations to graded rings and modules); © local algebra. Because most of these topics have either their source or their best motivation in algebraic geom­ etry, the algebro-geometric connections and applications of the purely algebraic material are constantly stressed and abundantly scattered through­ out the exposition.

    Combinatorial Aspects of Commutative Algebra and Algebraic Geometry: The Abel Symposium 2009 (Repost)

    Posted By: AvaxGenius
    Combinatorial Aspects of Commutative Algebra and Algebraic Geometry: The Abel Symposium 2009 (Repost)

    Combinatorial Aspects of Commutative Algebra and Algebraic Geometry: The Abel Symposium 2009 by Gunnar Fløystad, Trygve Johnsen, Andreas Leopold Knutsen
    English | PDF | 2011 | 186 Pages | ISBN : 3642194915 | 2.6 MB

    The Abel Symposium 2009 "Combinatorial aspects of Commutative Algebra and Algebraic Geometry", held at Voss, Norway, featured talks by leading researchers in the field.

    Approximation Theorems in Commutative Algebra: Classical and Categorical Methods

    Posted By: AvaxGenius
    Approximation Theorems in Commutative Algebra: Classical and Categorical Methods

    Approximation Theorems in Commutative Algebra: Classical and Categorical Methods by J. Alajbegović , J. Močkoř
    English | PDF | 1992 | 339 Pages | ISBN : 0792319486 | 43.3 MB

    Various types of approximation theorems are frequently used in general commutative algebra, and they have been found to be useful tools in valuation theory, the theory of Abelian lattice ordered groups, multiplicative ideal theory, etc.
    Part 1 of this volume is devoted to the investigation of approximation theorems from a classical point of view. The chapters of this part deal with fields and rings, partly ordered groups, and with multirings and d-groups.

    Ideals, Varieties, and Algorithms

    Posted By: AvaxGenius
    Ideals, Varieties, and Algorithms

    Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra by David A. Cox , John Little , Donal O’Shea
    English | PDF(True) | 2015 | 653 Pages | ISBN : 3319167200 | 9.6 MB

    This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the Preface illustrates a variety of ways to proceed with the material once these chapters are covered. In addition to the fundamentals of algebraic geometry—the elimination theorem, the extension theorem, the closure theorem and the Nullstellensatz—this new edition incorporates several substantial changes, all of which are listed in the Preface. The largest revision incorporates a new Chapter (ten), which presents some of the essentials of progress made over the last decades in computing Gröbner bases. The book also includes current computer algebra material in Appendix C and updated independent projects (Appendix D).