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Constructive Commutative Algebra
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Book Synopsis Commutative Algebra: Constructive Methods by : Henri Lombardi
Download or read book Commutative Algebra: Constructive Methods written by Henri Lombardi and published by Springer. This book was released on 2015-07-22 with total page 1033 pages. Available in PDF, EPUB and Kindle. Book excerpt: Translated from the popular French edition, this book offers a detailed introduction to various basic concepts, methods, principles, and results of commutative algebra. It takes a constructive viewpoint in commutative algebra and studies algorithmic approaches alongside several abstract classical theories. Indeed, it revisits these traditional topics with a new and simplifying manner, making the subject both accessible and innovative. The algorithmic aspects of such naturally abstract topics as Galois theory, Dedekind rings, Prüfer rings, finitely generated projective modules, dimension theory of commutative rings, and others in the current treatise, are all analysed in the spirit of the great developers of constructive algebra in the nineteenth century. This updated and revised edition contains over 350 well-arranged exercises, together with their helpful hints for solution. A basic knowledge of linear algebra, group theory, elementary number theory as well as the fundamentals of ring and module theory is required. Commutative Algebra: Constructive Methods will be useful for graduate students, and also researchers, instructors and theoretical computer scientists.
Book Synopsis Constructive Commutative Algebra by : Ihsen Yengui
Download or read book Constructive Commutative Algebra written by Ihsen Yengui and published by Springer. This book was released on 2015-12-11 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Gröbner 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 Zorn's 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.
Book Synopsis Commutative Algebra by : David Eisenbud
Download or read book Commutative Algebra written by David Eisenbud and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.
Book Synopsis A Course in Constructive Algebra by : Ray Mines
Download or read book A Course in Constructive Algebra written by Ray Mines and published by Springer Science & Business Media. This book was released on 2012-09-10 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: The constructive approach to mathematics has enjoyed a renaissance, caused in large part by the appearance of Errett Bishop's book Foundations of constr"uctiue analysis in 1967, and by the subtle influences of the proliferation of powerful computers. Bishop demonstrated that pure mathematics can be developed from a constructive point of view while maintaining a continuity with classical terminology and spirit; much more of classical mathematics was preserved than had been thought possible, and no classically false theorems resulted, as had been the case in other constructive schools such as intuitionism and Russian constructivism. The computers created a widespread awareness of the intuitive notion of an effecti ve procedure, and of computation in principle, in addi tion to stimulating the study of constructive algebra for actual implementation, and from the point of view of recursive function theory. In analysis, constructive problems arise instantly because we must start with the real numbers, and there is no finite procedure for deciding whether two given real numbers are equal or not (the real numbers are not discrete) . The main thrust of constructive mathematics was in the direction of analysis, although several mathematicians, including Kronecker and van der waerden, made important contributions to construc tive algebra. Heyting, working in intuitionistic algebra, concentrated on issues raised by considering algebraic structures over the real numbers, and so developed a handmaiden'of analysis rather than a theory of discrete algebraic structures.
Book Synopsis Constructive Commutative Algebra in Nonlinear Control Theory by : Krister Forsman
Download or read book Constructive Commutative Algebra in Nonlinear Control Theory written by Krister Forsman and published by . This book was released on 1991 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Wolmer Vasconcelos Publisher :Springer Science & Business Media ISBN 13 :9783540213116 Total Pages :432 pages Book Rating :4.2/5 (131 download)
Book Synopsis Computational Methods in Commutative Algebra and Algebraic Geometry by : Wolmer Vasconcelos
Download or read book Computational Methods in Commutative Algebra and Algebraic Geometry written by Wolmer Vasconcelos and published by Springer Science & Business Media. This book was released on 2004-05-18 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ACM volume deals with tackling problems that can be represented by data structures which are essentially matrices with polynomial entries, mediated by the disciplines of commutative algebra and algebraic geometry. The discoveries stem from an interdisciplinary branch of research which has been growing steadily over the past decade. The author covers a wide range, from showing how to obtain deep heuristics in a computation of a ring, a module or a morphism, to developing means of solving nonlinear systems of equations - highlighting the use of advanced techniques to bring down the cost of computation. Although intended for advanced students and researchers with interests both in algebra and computation, many parts may be read by anyone with a basic abstract algebra course.
Book Synopsis An Introduction to Commutative Algebra by : Huishi Li
Download or read book An Introduction to Commutative Algebra written by Huishi Li and published by World Scientific. This book was released on 2004 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: - Contains many examples and problems (with hints) - Provides a good introduction for beginners in algebraic number theory and algebraic geometry
Book Synopsis Algebraic Geometry and Commutative Algebra by : Hiroaki Hijikata
Download or read book Algebraic Geometry and Commutative Algebra written by Hiroaki Hijikata and published by Academic Press. This book was released on 2014-05-10 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic Geometry and Commutative Algebra in Honor of Masayoshi Nagata presents a collection of papers on algebraic geometry and commutative algebra in honor of Masayoshi Nagata for his significant contributions to commutative algebra. Topics covered range from power series rings and rings of invariants of finite linear groups to the convolution algebra of distributions on totally disconnected locally compact groups. The discussion begins with a description of several formulas for enumerating certain types of objects, which may be tabular arrangements of integers called Young tableaux or some types of monomials. The next chapter explains how to establish these enumerative formulas, with emphasis on the role played by transformations of determinantal polynomials and recurrence relations satisfied by them. The book then turns to several applications of the enumerative formulas and universal identity, including including enumerative proofs of the straightening law of Doubilet-Rota-Stein and computations of Hilbert functions of polynomial ideals of certain determinantal loci. Invariant differentials and quaternion extensions are also examined, along with the moduli of Todorov surfaces and the classification problem of embedded lines in characteristic p. This monograph will be a useful resource for practitioners and researchers in algebra and geometry.
Book Synopsis Introduction to Commutative Algebra and Algebraic Geometry by : Ernst Kunz
Download or read book Introduction to Commutative Algebra and Algebraic Geometry written by Ernst Kunz and published by Springer Science & Business Media. This book was released on 2012-11-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1985, this classic textbook is an English translation of Einführung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhäuser Classics series, the publisher is proud to make Introduction to Commutative Algebra and Algebraic Geometry available to a wider audience. Aimed at students who have taken a basic course in algebra, the goal of the text is to present important results concerning the representation of algebraic varieties as intersections of the least possible number of hypersurfaces and—a closely related problem—with the most economical generation of ideals in Noetherian rings. Along the way, one encounters many basic concepts of commutative algebra and algebraic geometry and proves many facts which can then serve as a basic stock for a deeper study of these subjects.
Download or read book Gröbner Bases written by Thomas Becker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: The origins of the mathematics in this book date back more than two thou sand years, as can be seen from the fact that one of the most important algorithms presented here bears the name of the Greek mathematician Eu clid. The word "algorithm" as well as the key word "algebra" in the title of this book come from the name and the work of the ninth-century scientist Mohammed ibn Musa al-Khowarizmi, who was born in what is now Uzbek istan and worked in Baghdad at the court of Harun al-Rashid's son. The word "algorithm" is actually a westernization of al-Khowarizmi's name, while "algebra" derives from "al-jabr," a term that appears in the title of his book Kitab al-jabr wa'l muqabala, where he discusses symbolic methods for the solution of equations. This close connection between algebra and al gorithms lasted roughly up to the beginning of this century; until then, the primary goal of algebra was the design of constructive methods for solving equations by means of symbolic transformations. During the second half of the nineteenth century, a new line of thought began to enter algebra from the realm of geometry, where it had been successful since Euclid's time, namely, the axiomatic method.
Book Synopsis Approximate Commutative Algebra by : Lorenzo Robbiano
Download or read book Approximate Commutative Algebra written by Lorenzo Robbiano and published by Springer Science & Business Media. This book was released on 2009-09-18 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approximate Commutative Algebra is an emerging field of research which endeavours to bridge the gap between traditional exact Computational Commutative Algebra and approximate numerical computation. The last 50 years have seen enormous progress in the realm of exact Computational Commutative Algebra, and given the importance of polynomials in scientific modelling, it is very natural to want to extend these ideas to handle approximate, empirical data deriving from physical measurements of phenomena in the real world. In this volume nine contributions from established researchers describe various approaches to tackling a variety of problems arising in Approximate Commutative Algebra.
Book Synopsis Commutative Algebra by : Irena Peeva
Download or read book Commutative Algebra written by Irena Peeva and published by Springer Science & Business Media. This book was released on 2013-02-01 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover 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. The book aims to showcase the area, especially for the benefit of junior mathematicians and researchers who are new to the field; it will aid them in broadening their background and to gain a deeper understanding of the current research in this area. Exciting developments are surveyed and many open problems are discussed with the aspiration to inspire the readers and foster further research.
Book Synopsis Commutative Algebra by : James Thomson Knight
Download or read book Commutative Algebra written by James Thomson Knight and published by Cambridge University Press. This book was released on 1971-10-31 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to commutative algebra gives an account of some general properties of rings and modules, with their applications to number theory and geometry. It assumes only that the reader has completed an undergraduate algebra course. The fresh approach and simplicity of proof enable a large amount of material to be covered; exercises and examples are included throughout the notes.
Book Synopsis Three Lectures on Commutative Algebra by : Holger Brenner
Download or read book Three Lectures on Commutative Algebra written by Holger Brenner and published by American Mathematical Soc.. This book was released on 2008 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures provides detailed introductions to some of the latest advances in three significant areas of rapid development in commutative algebra and its applications: tight closure and vector bundles; combinatorics and commutative algebra; constructive desingularization."
Book Synopsis A Singular Introduction to Commutative Algebra by : Gert-Martin Greuel
Download or read book A Singular Introduction to Commutative Algebra written by Gert-Martin Greuel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book can be understood as a model for teaching commutative algebra, and takes into account modern developments such as algorithmic and computational aspects. As soon as a new concept is introduced, the authors show how the concept can be worked on using a computer. The computations are exemplified with the computer algebra system Singular, developed by the authors. Singular is a special system for polynomial computation with many features for global as well as for local commutative algebra and algebraic geometry. The book includes a CD containing Singular as well as the examples and procedures explained in the book.
Book Synopsis Constructive Commutative Algebra in Nolinear Control Theory by :
Download or read book Constructive Commutative Algebra in Nolinear Control Theory written by and published by . This book was released on 1991 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Ideals, Varieties, and Algorithms by : David Cox
Download or read book Ideals, Varieties, and Algorithms written by David Cox and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. Contains a new section on Axiom and an update about MAPLE, Mathematica and REDUCE.
