Commutative Ring Theory
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Commutative Ring Theory
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Author : H. Matsumura
language : en
Publisher: Cambridge University Press
Release Date : 1989-05-25
Commutative Ring Theory written by H. Matsumura and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-05-25 with Mathematics categories.
In addition to being an interesting and profound subject in its own right, commutative ring theory is important as a foundation for algebraic geometry and complex analytical geometry. Matsumura covers the basic material, including dimension theory, depth, Cohen-Macaulay rings, Gorenstein rings, Krull rings and valuation rings. More advanced topics such as Ratliff's theorems on chains of prime ideals are also explored. The work is essentially self-contained, the only prerequisite being a sound knowledge of modern algebra, yet the reader is taken to the frontiers of the subject. Exercises are provided at the end of each section and solutions or hints to some of them are given at the end of the book.
Steps In Commutative Algebra
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Author : R. Y. Sharp
language : en
Publisher: Cambridge University Press
Release Date : 2000
Steps In Commutative Algebra written by R. Y. Sharp and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Introductory account of commutative algebra, aimed at students with a background in basic algebra.
Advances In Commutative Ring Theory
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Author : David Dobbs
language : en
Publisher: CRC Press
Release Date : 2023-08-25
Advances In Commutative Ring Theory written by David Dobbs and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-25 with Mathematics categories.
"Presents the proceedings of the recently held Third International Conference on Commutative Ring Theory in Fez, Morocco. Details the latest developments in commutative algebra and related areas-featuring 26 original research articles and six survey articles on fundamental topics of current interest. Examines wide-ranging developments in commutative algebra, together with connections to algebraic number theory and algebraic geometry."
Commutative Ring Theory
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Author : Paul-Jean Cahen
language : en
Publisher: CRC Press
Release Date : 1996-10-22
Commutative Ring Theory written by Paul-Jean Cahen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-10-22 with Mathematics categories.
Presents the proceedings of the Second International Conference on Commutative Ring Theory in Fes, Morocco. The text details developments in commutative algebra, highlighting the theory of rings and ideals. It explores commutative algebra's connections with and applications to topological algebra and algebraic geometry.
Commutative Ring Theory And Applications
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Author : Marco Fontana
language : en
Publisher: CRC Press
Release Date : 2017-07-27
Commutative Ring Theory And Applications written by Marco Fontana and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-27 with Mathematics categories.
Featuring presentations from the Fourth International Conference on Commutative Algebra held in Fez, Morocco, this reference presents trends in the growing area of commutative algebra. With contributions from nearly 50 internationally renowned researchers, the book emphasizes innovative applications and connections to algebraic number theory, geome
Commutative Ring Theory
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Author : Paul-Jean Cahen
language : en
Publisher: CRC Press
Release Date : 2023-06-14
Commutative Ring Theory written by Paul-Jean Cahen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-14 with Mathematics categories.
" Exploring commutative algebra's connections with and applications to topological algebra and algebraic geometry, Commutative Ring Theory covers the spectra of rings chain conditions, dimension theory, and Jaffard rings fiber products group rings, semigroup rings, and graded rings class groups linear groups integer-valued polynomials rings of finite fractions big Cohen-Macaulay modules and much more!"
Advances In Commutative Ring Theory
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Author : David E. Dobbs
language : en
Publisher:
Release Date : 1999
Advances In Commutative Ring Theory written by David E. Dobbs and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with MATHEMATICS categories.
Non Noetherian Commutative Ring Theory
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Author : S.T. Chapman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Non Noetherian Commutative Ring Theory written by S.T. Chapman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Commutative Ring Theory emerged as a distinct field of research in math ematics only at the beginning of the twentieth century. It is rooted in nine teenth century major works in Number Theory and Algebraic Geometry for which it provided a useful tool for proving results. From this humble origin, it flourished into a field of study in its own right of an astonishing richness and interest. Nowadays, one has to specialize in an area of this vast field in order to be able to master its wealth of results and come up with worthwhile contributions. One of the major areas of the field of Commutative Ring Theory is the study of non-Noetherian rings. The last ten years have seen a lively flurry of activity in this area, including: a large number of conferences and special sections at national and international meetings dedicated to presenting its results, an abundance of articles in scientific journals, and a substantial number of books capturing some of its topics. This rapid growth, and the occasion of the new Millennium, prompted us to embark on a project aimed at presenting an overview of the recent research in the area. With this in mind, we invited many of the most prominent researchers in Non-Noetherian Commutative Ring Theory to write expository articles representing the most recent topics of research in this area.
Foundations Of Commutative Rings And Their Modules
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Author : Fanggui Wang
language : en
Publisher: Springer
Release Date : 2017-01-06
Foundations Of Commutative Rings And Their Modules written by Fanggui Wang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-06 with Mathematics categories.
This book provides an introduction to the basics and recent developments of commutative algebra. A glance at the contents of the first five chapters shows that the topics covered are ones that usually are included in any commutative algebra text. However, the contents of this book differ significantly from most commutative algebra texts: namely, its treatment of the Dedekind–Mertens formula, the (small) finitistic dimension of a ring, Gorenstein rings, valuation overrings and the valuative dimension, and Nagata rings. Going further, Chapter 6 presents w-modules over commutative rings as they can be most commonly used by torsion theory and multiplicative ideal theory. Chapter 7 deals with multiplicative ideal theory over integral domains. Chapter 8 collects various results of the pullbacks, especially Milnor squares and D+M constructions, which are probably the most important example-generating machines. In Chapter 9, coherent rings with finite weak global dimensions are probed, and the local ring of weak global dimension two is elaborated on by combining homological tricks and methods of star operation theory. Chapter 10 is devoted to the Grothendieck group of a commutative ring. In particular, the Bass–Quillen problem is discussed. Finally, Chapter 11 aims to introduce relative homological algebra, especially where the related concepts of integral domains which appear in classical ideal theory are defined and investigated by using the class of Gorenstein projective modules. Each section of the book is followed by a selection of exercises of varying degrees of difficulty. This book will appeal to a wide readership from graduate students to academic researchers who are interested in studying commutative algebra.
Commutative Ring Theory
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Author : Paul-Jean Cahen
language : en
Publisher:
Release Date : 1994
Commutative Ring Theory written by Paul-Jean Cahen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with MATHEMATICS categories.
Exploring commutative algebra's connections with and applications to topological algebra and algebraic geometry, Commutative Ring Theory covers the spectra of rings chain conditions, dimension theory, and Jaffard rings fiber products group rings, semigroup rings, and graded rings class groups linear groups integer-valued polynomials rings of finite fractions big Cohen-Macaulay modules and much more!