Linear Algebra over Commutative Rings PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Linear Algebra over Commutative Rings PDF full book. Access full book title Linear Algebra over Commutative Rings by Bernard R. McDonald. Download full books in PDF and EPUB format.
Author: Bernard R. McDonald
Publisher: CRC Press
ISBN: 1000146464
Category : Mathematics
Languages : en
Pages : 564
Get Book Here
Book Description
This monograph arose from lectures at the University of Oklahoma on topics related to linear algebra over commutative rings. It provides an introduction of matrix theory over commutative rings. The monograph discusses the structure theory of a projective module.
Author: Bernard R. McDonald
Publisher: CRC Press
ISBN: 1000146464
Category : Mathematics
Languages : en
Pages : 564
Get Book Here
Book Description
This monograph arose from lectures at the University of Oklahoma on topics related to linear algebra over commutative rings. It provides an introduction of matrix theory over commutative rings. The monograph discusses the structure theory of a projective module.
Author: Bernard R. McDonald
Publisher: CRC Press
ISBN: 1000110613
Category : Mathematics
Languages : en
Pages : 561
Get Book Here
Book Description
This monograph arose from lectures at the University of Oklahoma on topics related to linear algebra over commutative rings. It provides an introduction of matrix theory over commutative rings. The monograph discusses the structure theory of a projective module.
Author: Aleks Kleyn
Publisher: CreateSpace
ISBN: 9781499324006
Category : Mathematics
Languages : en
Pages : 108
Get Book Here
Book Description
In this book I treat linear maps of vector space over division ring. The set of linear maps of left vector space over division ring D is right vector space over division ring D. The concept of twin representations follows from the joint consideration of vector space V and vector space of linear transformations of the vector space V. Considering of twin representations of division ring in Abelian group leads to the concept of D-vector space and their linear map. Based on polylinear map I considered definition of tensor product of rings and tensor product of D-vector spaces.
Author: Antoine Chambert-Loir
Publisher: Springer Nature
ISBN: 3030615952
Category : Mathematics
Languages : en
Pages : 466
Get Book Here
Book Description
This book stems from lectures on commutative algebra for 4th-year university students at two French universities (Paris and Rennes). At that level, students have already followed a basic course in linear algebra and are essentially fluent with the language of vector spaces over fields. The topics introduced include arithmetic of rings, modules, especially principal ideal rings and the classification of modules over such rings, Galois theory, as well as an introduction to more advanced topics such as homological algebra, tensor products, and algebraic concepts involved in algebraic geometry. More than 300 exercises will allow the reader to deepen his understanding of the subject. The book also includes 11 historical vignettes about mathematicians who contributed to commutative algebra.
Author: Martin Kreuzer
Publisher: Springer
ISBN: 3319436015
Category : Mathematics
Languages : en
Pages : 332
Get Book Here
Book Description
This book combines, in a novel and general way, an extensive development of the theory of families of commuting matrices with applications to zero-dimensional commutative rings, primary decompositions and polynomial system solving. It integrates the Linear Algebra of the Third Millennium, developed exclusively here, with classical algorithmic and algebraic techniques. Even the experienced reader will be pleasantly surprised to discover new and unexpected aspects in a variety of subjects including eigenvalues and eigenspaces of linear maps, joint eigenspaces of commuting families of endomorphisms, multiplication maps of zero-dimensional affine algebras, computation of primary decompositions and maximal ideals, and solution of polynomial systems. This book completes a trilogy initiated by the uncharacteristically witty books Computational Commutative Algebra 1 and 2 by the same authors. The material treated here is not available in book form, and much of it is not available at all. The authors continue to present it in their lively and humorous style, interspersing core content with funny quotations and tongue-in-cheek explanations.
Author: David Eisenbud
Publisher: Springer Science & Business Media
ISBN: 1461253500
Category : Mathematics
Languages : en
Pages : 784
Get Book Here
Book Description
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.
Author: Henri Lombardi
Publisher: Springer
ISBN: 940179944X
Category : Mathematics
Languages : en
Pages : 1033
Get Book Here
Book Description
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.
Author: Hideyuki Matsumura
Publisher: Cambridge University Press
ISBN: 9780521367646
Category : Mathematics
Languages : en
Pages : 338
Get Book Here
Book Description
This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.
Author: Joachim Lambek
Publisher:
ISBN:
Category : Associative rings
Languages : en
Pages : 206
Get Book Here
Book Description
Author: Marco Fontana
Publisher: Springer Science & Business Media
ISBN: 144196990X
Category : Mathematics
Languages : en
Pages : 491
Get Book Here
Book Description
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. This volume contains a collection of invited survey articles by some of the leading experts in the field. The authors of these chapters have been carefully selected for their important contributions to an area of commutative-algebraic research. Some topics presented in the volume include: generalizations of cyclic modules, zero divisor graphs, class semigroups, forcing algebras, syzygy bundles, tight closure, Gorenstein dimensions, tensor products of algebras over fields, as well as many others. This book is intended for researchers and graduate students interested in studying the many topics related to commutative algebra.
