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Algèbre commutative, Chapitres 1 à 4 Les Éléments de mathématique de Nicolas BOURBAKI ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements. Ce premier volume du Livre d’Algèbre commutative, septième Livre du traité, est consacré aux concepts fondamentaux de l’algèbre commutative. Il comprend les chapitres : Modules plats ; Localisation ; Graduations, filtrations et topologies ; Idéaux premiers associés et décomposition primaire. Il contient également des notes historiques. Ce volume est une réimpression de l’édition de 1969.

Commutative algebra. --- Algebra --- Algebra. --- Commutative Rings and Algebras. --- Mathematics --- Mathematical analysis --- Commutative rings. --- Rings (Algebra)

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Algèbre commutative, Chapitres 5 à 7 Les Éléments de mathématique de Nicolas BOURBAKI ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements. Ce deuxième volume du Livre d’Algèbre commutative, septième Livre du traité, introduit deux notions fondamentales en algèbre commutative, celle d’entier algébrique et celle de valuation, qui ont de nombreuses applications en théorie des nombres et en géometrie algébrique. It traite également des anneaux de Krull ou de Dedekind. Il comprend les chapitres : Entiers ; Valuations ; Diviseurs. Il contient également des notes historiques. Ce volume est une réimpression de l’édition de 1965.

Mathematics. --- Commutative algebra. --- Commutative rings. --- Commutative Rings and Algebras. --- Algebra. --- Mathematics --- Mathematical analysis --- Rings (Algebra) --- Algebra

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A polarised variety is a modern generalization of the notion of a variety in classical algebraic geometry. It consists of a pair: the algebraic variety itself, together with an ample line bundle on it. Using techniques from abstract algebraic geometry that have been developed over recent decades, Professor Fujita develops classification theories of such pairs using invariants that are polarised higher-dimensional versions of the genus of algebraic curves. The heart of the book is the theory of D-genus and sectional genus developed by the author, but numerous related topics are discussed or surveyed. Proofs are given in full in the central part of the development, but background and technical results are sometimes just sketched when the details are not essential for understanding the key ideas. Readers are assumed to have some background in algebraic geometry, including sheaf cohomology, and for them this work will provide an illustration of the power of modern abstract techniques applied to concrete geometric problems. Thus the book helps the reader not only to understand about classical objects but also modern methods, and so it will be useful not only for experts but also non-specialists and graduate students.

Algebraic varieties --- Classification theory of algebraic varieties --- Classification theory. --- #KVIV:BB --- 512.7 --- 512.7 Algebraic geometry. Commutative rings and algebras --- Algebraic geometry. Commutative rings and algebras --- Classification theory

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Nato dai corsi universitari di Teoria dei Gruppi tenuti per vari anni dall'autore, questo libro affronta gli argomenti fondamentali della teoria: gruppi abeliani, nilpotenti e risolubili, gruppi liberi, permutazioni, rappresentazioni e coomologia. Dopo le prime nozioni, viene esposto il programma di Hölder per la classificazione dei gruppi finiti. Un lungo capitolo è dedicato all'azione di un gruppo su un insieme e alle permutazioni, sia sotto l'aspetto algebrico che combinatorio, con richiami alla teoria delle equazioni. Si considerano anche alcune questioni di carattere logico, come la decidibilità del problema della parola per certe classi di gruppi. Un aspetto essenziale del libro è la presenza di una grande varietà di esercizi, circa 400, in gran parte risolti. .

Mathematics. --- Algebra. --- Commutative algebra. --- Commutative rings. --- Group theory. --- Group Theory and Generalizations. --- Commutative Rings and Algebras. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Mathematics --- Mathematical analysis --- Rings (Algebra)

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The subject of this book is the solution of polynomial equations, that is, s- tems of (generally) non-linear algebraic equations. This study is at the heart of several areas of mathematics and its applications. It has provided the - tivation for advances in di?erent branches of mathematics such as algebra, geometry, topology, and numerical analysis. In recent years, an explosive - velopment of algorithms and software has made it possible to solve many problems which had been intractable up to then and greatly expanded the areas of applications to include robotics, machine vision, signal processing, structural molecular biology, computer-aided design and geometric modelling, as well as certain areas of statistics, optimization and game theory, and b- logical networks. At the same time, symbolic computation has proved to be an invaluable tool for experimentation and conjecture in pure mathematics. As a consequence, the interest in e?ective algebraic geometry and computer algebrahasextendedwellbeyonditsoriginalconstituencyofpureandapplied mathematicians and computer scientists, to encompass many other scientists and engineers. While the core of the subject remains algebraic geometry, it also calls upon many other aspects of mathematics and theoretical computer science, ranging from numerical methods, di?erential equations and number theory to discrete geometry, combinatorics and complexity theory. Thegoalofthisbookistoprovideageneralintroduction tomodernma- ematical aspects in computing with multivariate polynomials and in solving algebraic systems.

Equations --- Polynomials. --- Numerical solutions. --- Algebra --- Graphic methods --- Algebra. --- Algorithms. --- Symbolic and Algebraic Manipulation. --- Data processing. --- Algorism --- Arithmetic --- Mathematics --- Mathematical analysis --- Foundations --- Polynomials --- 512.7 --- 512.7 Algebraic geometry. Commutative rings and algebras --- Algebraic geometry. Commutative rings and algebras --- Numerical solutions --- Computer science—Mathematics.