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Constructive commutative algebra, Yengui, Ihsen



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Автор: Yengui, Ihsen
Название:  Constructive commutative algebra
ISBN: 9783319194936
Издательство: Springer
Классификация:
ISBN-10: 3319194933
Обложка/Формат: Paperback
Страницы: 271
Вес: 0.472 кг.
Дата издания: 12.12.2015
Серия: Lecture notes in mathematics
Язык: English
Иллюстрации: 5 black & white illustrations, biography
Размер: 236 x 156 x 21
Читательская аудитория: Professional & vocational
Подзаголовок: Projective modules over polynomial rings and dynamical greobner bases
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание:

The main goal of this book is to find the constructive content hidden in abstract proofs of concrete theorems in Commutative Algebra, especially in well-known theorems concerning projective modules over polynomial rings (mainly the Quillen-Suslin theorem) and syzygies of multivariate polynomials with coefficients in a valuation ring.

Simple and constructive proofs of some results in the theory of projective modules over polynomial rings are also given, and light is cast upon recent progress on the Hermite ring and Gr bner ring conjectures. New conjectures on unimodular completion arising from our constructive approach to the unimodular completion problem are presented.

Constructive algebra can be understood as a first preprocessing step for computer algebra that leads to the discovery of general algorithms, even if they are sometimes not efficient. From a logical point of view, the dynamical evaluation gives a constructive substitute for two highly nonconstructive tools of abstract algebra: the Law of Excluded Middle and Zorns Lemma. For instance, these tools are required in order to construct the complete prime factorization of an ideal in a Dedekind ring, whereas the dynamical method reveals the computational content of this construction. These lecture notes follow this dynamical philosophy.




Commutative Algebra and its Interactions to Algebraic Geometry

Автор: Tu CUONG
Название: Commutative Algebra and its Interactions to Algebraic Geometry
ISBN: 3319755641 ISBN-13(EAN): 9783319755649
Издательство: Springer
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Цена: 10713 р.
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Описание: This book presents four lectures on recent research in commutative algebra and its applications to algebraic geometry. The first lecture is on Weyl algebras (certain rings of differential operators) and their D-modules, relating non-commutative and commutative algebra to algebraic geometry and analysis in a very appealing way.

A Course in Constructive Algebra

Автор: Mines
Название: A Course in Constructive Algebra
ISBN: 0387966404 ISBN-13(EAN): 9780387966403
Издательство: Springer
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Цена: 13774 р.
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Описание: Presents the fundamental structures of modern algebra from a constructive point of view. This book contains basic notions, and also covers PID`s, field theory (including Galois theory), factorisation of polynomials, noetherian rings, valuation theory, and Dedekind domains.

Multiplicative Ideal Theory in Commutative Algebra

Автор: James W. Brewer; Sarah Glaz; William Heinzer; Bruc
Название: Multiplicative Ideal Theory in Commutative Algebra
ISBN: 1441937552 ISBN-13(EAN): 9781441937551
Издательство: Springer
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Цена: 23724 р.
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Описание: This volume, a tribute to the work of Robert Gilmer, consists of twenty-four articles authored by his most prominent students and followers. These articles combine surveys of past work by Gilmer and others, recent results which have never before seen print, open problems, and extensive bibliographies.

Computational Commutative Algebra 2

Автор: Martin Kreuzer; Lorenzo Robbiano
Название: Computational Commutative Algebra 2
ISBN: 3642064914 ISBN-13(EAN): 9783642064913
Издательство: Springer
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Цена: 9182 р.
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Описание: "The second volume of the authors` `Computational commutative algebra`...covers on its 586 pages a wealth of interesting material with several unexpected applications. The text is recommended for all those who want to learn and enjoy an algebraic tool that becomes more and more relevant to different fields of applications."

Commutative Algebra

Автор: Marco Fontana; Sophie Frisch; Sarah Glaz
Название: Commutative Algebra
ISBN: 1493947419 ISBN-13(EAN): 9781493947416
Издательство: Springer
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Цена: 14540 р.
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Описание:

This volume presents a multi-dimensional collection of articles highlighting recent developments in commutative algebra. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics and research methods include Noetherian and non- Noetherian ring theory as well as integer-valued polynomials and functions.

Specific topics include:

- Homological dimensions of Prufer-like rings

- Quasi complete rings

- Total graphs of rings

- Properties of prime ideals over various rings

- Bases for integer-valued polynomials

- Boolean subrings

- The portable property of domains

- Probabilistic topics in Intn(D)

- Closure operations in Zariski-Riemann spaces of valuation domains

- Stability of domains

- Non-Noetherian grade

- Homotopy in integer-valued polynomials

- Localizations of global properties of rings

- Topics in integral closure

- Monoids and submonoids of domains

The book includes twenty articles written by many of the most prominent researchers in the field. Most contributions are authored by attendees of the conference in commutative algebra held at the Graz University of Technology in December 2012. There is also a small collection of invited articles authored by those who did not attend the conference. Following the model of the Graz conference, the volume contains a number of comprehensive survey articles along with related research articles featuring recent results that have not yet been published elsewhere.

Commutative Algebra

Автор: Marco Fontana; Salah-Eddine Kabbaj; Bruce Olberdin
Название: Commutative Algebra
ISBN: 1489990046 ISBN-13(EAN): 9781489990044
Издательство: Springer
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Цена: 28315 р.
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Описание: Commutative Algebra presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutative algebra. Topics include generalizations of cyclic modules, zero divisor graphs, class semigroups, forcing algebras, syzygy bundles, tight closure, Gorenstein dimensions, and more.

A Singular Introduction to Commutative Algebra

Автор: O. Bachmann; Gert-Martin Greuel; C. Lossen; Gerhar
Название: A Singular Introduction to Commutative Algebra
ISBN: 3642442544 ISBN-13(EAN): 9783642442544
Издательство: Springer
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Цена: 9948 р.
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Описание: This substantially enlarged second edition aims to lead a further stage in the computational revolution in commutative algebra. Another feature of the book is its breadth of coverage of theoretical topics in the portions of commutative algebra closest to algebraic geometry, with algorithmic treatments of almost every topic.

Homological and Computational Methods in Commutative Algebra

Автор: Aldo Conca; Joseph Gubeladze; Tim R?mer
Название: Homological and Computational Methods in Commutative Algebra
ISBN: 331961942X ISBN-13(EAN): 9783319619422
Издательство: Springer
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Цена: 15305 р.
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Описание: This volume collects contributions by leading experts in the area of commutative algebra related to the INdAM meeting "Homological and Computational Methods in Commutative Algebra" held in Cortona (Italy) from May 30 to June 3, 2016 .

Commutative Algebra

Автор: Irena Peeva
Название: Commutative Algebra
ISBN: 1461452910 ISBN-13(EAN): 9781461452911
Издательство: Springer
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Цена: 27550 р.
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Описание: This volume covers a very wide range of topics, including core areas in commutative algebra and also relations to algebraic geometry, algebraic combinatorics, hyperplane arrangements, homological algebra, and string theory.

Commutative Algebra

Автор: Winfried Bruns; Aron Simis
Название: Commutative Algebra
ISBN: 3540527451 ISBN-13(EAN): 9783540527459
Издательство: Springer
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Цена: 3819 р.
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Описание: Describes commutative algebra with emphasis on special graded algebras, which are increasingly of interest in problems of algebraic geometry, combinatorics and computer algebra.


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