Topics In Commutative Ring Theory
DOWNLOAD
Download Topics In Commutative Ring Theory PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Topics In Commutative Ring Theory book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Topics In Commutative Ring Theory
DOWNLOAD
Author : John J. Watkins
language : en
Publisher: Princeton University Press
Release Date : 2009-02-09
Topics In Commutative Ring Theory written by John J. Watkins and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-09 with Mathematics categories.
Topics in Commutative Ring Theory is a textbook for advanced undergraduate students as well as graduate students and mathematicians seeking an accessible introduction to this fascinating area of abstract algebra. Commutative ring theory arose more than a century ago to address questions in geometry and number theory. A commutative ring is a set-such as the integers, complex numbers, or polynomials with real coefficients--with two operations, addition and multiplication. Starting from this simple definition, John Watkins guides readers from basic concepts to Noetherian rings-one of the most important classes of commutative rings--and beyond to the frontiers of current research in the field. Each chapter includes problems that encourage active reading--routine exercises as well as problems that build technical skills and reinforce new concepts. The final chapter is devoted to new computational techniques now available through computers. Careful to avoid intimidating theorems and proofs whenever possible, Watkins emphasizes the historical roots of the subject, like the role of commutative rings in Fermat's last theorem. He leads readers into unexpected territory with discussions on rings of continuous functions and the set-theoretic foundations of mathematics. Written by an award-winning teacher, this is the first introductory textbook to require no prior knowledge of ring theory to get started. Refreshingly informal without ever sacrificing mathematical rigor, Topics in Commutative Ring Theory is an ideal resource for anyone seeking entry into this stimulating field of study.
Advances In Commutative Ring Theory
DOWNLOAD
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."
Topics In The Homological Theory Of Modules Over Commutative Rings
DOWNLOAD
Author : Melvin Hochster
language : en
Publisher: American Mathematical Soc.
Release Date : 1975-12-31
Topics In The Homological Theory Of Modules Over Commutative Rings written by Melvin Hochster and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-12-31 with Mathematics categories.
This volume contains expository lectures by Melvin Hochster from the CBMS Regional Conference in Mathematics held at the University of Nebraska, June 1974. The lectures deal mainly with recent developments and still open questions in the homological theory of modules over commutative (usually, Noetherian) rings. A good deal of attention is given to the role ``big'' Cohen-Macaulay modules play in clearing up some of the open questions. A modest knowledge of commutative rings and familarity with (the long exact sequences for) Tor and Ext should suffice as a background for the reader.
Commutative Ring Theory
DOWNLOAD
Author : Paul-Jean Cahen
language : en
Publisher:
Release Date : 1997
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 1997 with MATHEMATICS categories.
Presenting the proceedings of the recently held Second International Conference on Commutative Ring Theory in Fes, Morocco, this up-to-date reference details the latest developments in commutative algebra - highlighting the theory of rings and ideals. Exploring commutative algebra's connections with and applications to topological algebra and algebraic geometry, Commutative Ring Theory covers spectra of rings ... dimension theory ... chain conditions ... class groups ... duals of ideals ... Mori and Krull domains ... Prufer domains ... integer-valued polynomials ... semigroup rings ... seminormalization and weak normalization ... generators of ideals ... homological aspects ... and more. Furnishing over 580 literature citations, allowing further in-depth study of particular topics, Commutative Ring Theory is a vital resource for research mathematicians, algebraists, commutative ring theorists, and graduate students in these disciplines.
Topics In Commutative Ring Theory
DOWNLOAD
Author : Irving Kaplansky
language : en
Publisher:
Release Date : 1974
Topics In Commutative Ring Theory written by Irving Kaplansky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Commutative rings categories.
Commutative Ring Theory
DOWNLOAD
Author : Hideyuki Matsumura
language : en
Publisher: Cambridge University Press
Release Date : 1989-05-25
Commutative Ring Theory written by Hideyuki 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.
This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.
Foundations Of Commutative Rings And Their Modules
DOWNLOAD
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 Algebra
DOWNLOAD
Author : Marco Fontana
language : en
Publisher: Springer
Release Date : 2014-07-15
Commutative Algebra written by Marco Fontana and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-15 with Mathematics categories.
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 Prüfer-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.
Topics In Group Rings
DOWNLOAD
Author : Sudarshan K. Sehgal
language : en
Publisher:
Release Date : 1978
Topics In Group Rings written by Sudarshan K. Sehgal and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Mathematics categories.
The group ring KG of the group G over a commutative unital ring K comprises an attractive object of study. This is one of the few algebraic structures that allow for explicit computations. Several easily formulated questions are associated with this topic. Many interesting results have been obtained in this area by using deep results and techniques from group theory, ring theory, and number theory. Most of the results presented and techniques used have a number theoretic flavor. Aimed at advanced graduate students and research mathematicians in algebra.
Non Noetherian Commutative Ring Theory
DOWNLOAD
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.