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)

Label
Foundations of Commutative Rings and Their Modules
Title
Foundations of Commutative Rings and Their Modules
Statement of responsibility
by Fanggui Wang, Hwankoo Kim
Creator
Contributor
Author
Provider
Subject
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 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
Member of
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)
Instantiates
Publication
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 w-Modules 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
10.1007/978-981-10-3337-7
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-981-10-3337-7
Label
Foundations of Commutative Rings and Their Modules, by Fanggui Wang, Hwankoo Kim, (electronic resource)
Publication
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 w-Modules 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
10.1007/978-981-10-3337-7
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-981-10-3337-7

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