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The Resource Foundations of Commutative Rings and Their Modules, by Fanggui Wang, Hwankoo Kim, (electronic resource)
Foundations of Commutative Rings and Their Modules, by Fanggui Wang, Hwankoo Kim, (electronic resource)
Resource Information
The item Foundations of Commutative Rings and Their Modules, by Fanggui Wang, Hwankoo Kim, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Foundations of Commutative Rings and Their Modules, by Fanggui Wang, Hwankoo Kim, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 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 wmodules 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 examplegenerating 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
 Language
 eng
 Extent
 XX, 699 p. 273 illus.
 Contents

 1 Basic Theory of Rings and Modules
 2 The Category of Modules
 3 Homological Methods
 4 Basic Theory of Noetherian Rings
 5 Extensions of Rings
 6 wModules over Commutative Rings
 7 Multiplicative Ideal Theory over Integral Domains
 8 Structural Theory of Milnor Squares
 9 Coherent Rings with Finite Weak Global Dimension
 10 The Grothendieck Group of a Ring
 11 Relative Homological Algebra
 References
 Index of Symbols
 Index
 Isbn
 9789811033377
 Label
 Foundations of Commutative Rings and Their Modules
 Title
 Foundations of Commutative Rings and Their Modules
 Statement of responsibility
 by Fanggui Wang, Hwankoo Kim
 Language
 eng
 Summary
 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 wmodules 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 examplegenerating 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
 http://library.link/vocab/creatorName
 Wang, Fanggui
 Image bit depth
 0
 LC call number
 QA251.3
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName

 Kim, Hwankoo.
 SpringerLink
 Series statement
 Algebra and Applications,
 Series volume
 22
 http://library.link/vocab/subjectName

 Mathematics
 Categories (Mathematics)
 Algebra, Homological
 Commutative algebra
 Commutative rings
 Mathematics
 Commutative Rings and Algebras
 Category Theory, Homological Algebra
 Label
 Foundations of Commutative Rings and Their Modules, by Fanggui Wang, Hwankoo Kim, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 1 Basic Theory of Rings and Modules  2 The Category of Modules  3 Homological Methods  4 Basic Theory of Noetherian Rings  5 Extensions of Rings  6 wModules over Commutative Rings  7 Multiplicative Ideal Theory over Integral Domains  8 Structural Theory of Milnor Squares  9 Coherent Rings with Finite Weak Global Dimension  10 The Grothendieck Group of a Ring  11 Relative Homological Algebra  References  Index of Symbols  Index
 Dimensions
 unknown
 Extent
 XX, 699 p. 273 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9789811033377
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9789811033377
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9789811033377
 Label
 Foundations of Commutative Rings and Their Modules, by Fanggui Wang, Hwankoo Kim, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 1 Basic Theory of Rings and Modules  2 The Category of Modules  3 Homological Methods  4 Basic Theory of Noetherian Rings  5 Extensions of Rings  6 wModules over Commutative Rings  7 Multiplicative Ideal Theory over Integral Domains  8 Structural Theory of Milnor Squares  9 Coherent Rings with Finite Weak Global Dimension  10 The Grothendieck Group of a Ring  11 Relative Homological Algebra  References  Index of Symbols  Index
 Dimensions
 unknown
 Extent
 XX, 699 p. 273 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9789811033377
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9789811033377
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9789811033377
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