Coverart for item
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
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
Assigning source
Provided by publisher
http://library.link/vocab/creatorName
Wang, Fanggui
Image bit depth
0
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Kim, Hwankoo
Series statement
  • Algebra and Applications,
  • Springer eBooks
  • Springer eBooks.
Series volume
22
http://library.link/vocab/subjectName
Algebra
Label
Foundations of Commutative Rings and Their Modules, by Fanggui Wang, Hwankoo Kim, (electronic resource)
Link
http://ezproxy.eui.eu/login?url=https://doi.org/10.1007/978-981-10-3337-7
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
Control code
978-981-10-3337-7
Dimensions
unknown
Extent
1 online resource (XXII, 699 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9789811033377
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
273 illustrations
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)968211955
Label
Foundations of Commutative Rings and Their Modules, by Fanggui Wang, Hwankoo Kim, (electronic resource)
Link
http://ezproxy.eui.eu/login?url=https://doi.org/10.1007/978-981-10-3337-7
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
Control code
978-981-10-3337-7
Dimensions
unknown
Extent
1 online resource (XXII, 699 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9789811033377
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
273 illustrations
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)968211955

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