LEADER 04083nam 22005655 450 001 9910159532103321 005 20250415004714.0 024 7 $a10.1007/978-981-10-3337-7 035 $a(CKB)3710000001008962 035 $a(DE-He213)978-981-10-3337-7 035 $a(MiAaPQ)EBC4778954 035 $a(PPN)198338600 035 $a(EXLCZ)993710000001008962 100 $a20170106d2016 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFoundations of Commutative Rings and Their Modules /$fby Fanggui Wang, Hwankoo Kim 205 $a1st ed. 2016. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2016. 215 $a1 online resource (XXII, 699 p. 273 illus.) 225 1 $aAlgebra and Applications,$x2192-2950 ;$v22 311 08$a981-10-3336-6 311 08$a981-10-3337-4 320 $aIncludes bibliographical references and index. 327 $a1 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. 330 $aThis book provides an introduction to the basics and recent developments of commutative algebra. A glance at the contents of the first five chapters shows that the topics covered are ones that usually are included in any commutative algebra text. However, the contents of this book differ significantly from most commutative algebra texts: namely, its treatment of the Dedekind?Mertens formula, the (small) finitistic dimension of a ring, Gorenstein rings, valuation overrings and the valuative dimension, and Nagata rings. Going further, Chapter 6 presents w-modules over commutative rings as they can be most commonly used by torsion theory and multiplicative ideal theory. Chapter 7 deals with multiplicative ideal theory over integral domains. Chapter 8 collects various results of the pullbacks, especially Milnor squares and D+M constructions, which are probably the most important example-generating machines. In Chapter 9, coherent rings with finite weak global dimensions are probed, and thelocal ring of weak global dimension two is elaborated on by combining homological tricks and methods of star operation theory. Chapter 10 is devoted to the Grothendieck group of a commutative ring. In particular, the Bass?Quillen problem is discussed. Finally, Chapter 11 aims to introduce relative homological algebra, especially where the related concepts of integral domains which appear in classical ideal theory are defined and investigated by using the class of Gorenstein projective modules. Each section of the book is followed by a selection of exercises of varying degrees of difficulty. This book will appeal to a wide readership from graduate students to academic researchers who are interested in studying commutative algebra. 410 0$aAlgebra and Applications,$x2192-2950 ;$v22 606 $aCommutative algebra 606 $aCommutative rings 606 $aAlgebra, Homological 606 $aCommutative Rings and Algebras 606 $aCategory Theory, Homological Algebra 615 0$aCommutative algebra. 615 0$aCommutative rings. 615 0$aAlgebra, Homological. 615 14$aCommutative Rings and Algebras. 615 24$aCategory Theory, Homological Algebra. 676 $a512.4 700 $aWang$b Fanggui$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755915 702 $aKim$b Hwankoo$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910159532103321 996 $aFoundations of Commutative Rings and Their Modules$92047105 997 $aUNINA