Foundations of Commutative Rings and Their Modules

Nonfiction, Science & Nature, Mathematics, Algebra, History
Cover of the book Foundations of Commutative Rings and Their Modules by Fanggui Wang, Hwankoo Kim, Springer Singapore
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Fanggui Wang, Hwankoo Kim ISBN: 9789811033377
Publisher: Springer Singapore Publication: January 6, 2017
Imprint: Springer Language: English
Author: Fanggui Wang, Hwankoo Kim
ISBN: 9789811033377
Publisher: Springer Singapore
Publication: January 6, 2017
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer Singapore

Cover of the book Corporate Social Responsibility in India by Fanggui Wang, Hwankoo Kim
Cover of the book Environmental Regulations and Innovation in Advanced Automobile Technologies by Fanggui Wang, Hwankoo Kim
Cover of the book The Indian Metamorphosis by Fanggui Wang, Hwankoo Kim
Cover of the book Auction Based Resource Provisioning in Cloud Computing by Fanggui Wang, Hwankoo Kim
Cover of the book Topology Design of Robot Mechanisms by Fanggui Wang, Hwankoo Kim
Cover of the book The Language and Iconography of Chinese Charms by Fanggui Wang, Hwankoo Kim
Cover of the book Mathematical Models, Methods and Applications by Fanggui Wang, Hwankoo Kim
Cover of the book Korean Modernization and Uneven Development by Fanggui Wang, Hwankoo Kim
Cover of the book The Role of Water in ATP Hydrolysis Energy Transduction by Protein Machinery by Fanggui Wang, Hwankoo Kim
Cover of the book Smart Trends in Information Technology and Computer Communications by Fanggui Wang, Hwankoo Kim
Cover of the book Male Infertility: Understanding, Causes and Treatment by Fanggui Wang, Hwankoo Kim
Cover of the book Embedded System Technology by Fanggui Wang, Hwankoo Kim
Cover of the book Social Media Processing by Fanggui Wang, Hwankoo Kim
Cover of the book Biomaterials for Musculoskeletal Regeneration by Fanggui Wang, Hwankoo Kim
Cover of the book Synthesis of Zinc Oxide by Sol–Gel Method for Photoelectrochemical Cells by Fanggui Wang, Hwankoo Kim
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy