LEADER 04058nam 22005775 450 001 9910886090503321 005 20250415004657.0 010 $a981-9752-84-1 024 7 $a10.1007/978-981-97-5284-3 035 $a(MiAaPQ)EBC31642115 035 $a(Au-PeEL)EBL31642115 035 $a(CKB)34775346900041 035 $a(MiAaPQ)EBC31643258 035 $a(Au-PeEL)EBL31643258 035 $a(DE-He213)978-981-97-5284-3 035 $a(EXLCZ)9934775346900041 100 $a20240903d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFoundations of Commutative Rings and Their Modules /$fby Fanggui Wang, Hwankoo Kim 205 $a2nd ed. 2024. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2024. 215 $a1 online resource (862 pages) 225 1 $aAlgebra and Applications,$x2192-2950 ;$v31 311 08$a981-9752-83-3 327 $aBasic Theory of Rings and Modules -- Several Classical Module Classes in the Module Category -- Homological Methods -- Basic Theory of Noetherian Rings -- Extensions of Rings -- w-Modules over Rings -- Multiplicative Ideal Theory over Integral Domains -- Structural Theory of Milnor Squares -- Coherent Rings with Finite Weak Global Dimension -- Grothendieck Groups of Rings -- Relative Homological Algebra -- Cotorsion Theory. 330 $aThis book provides an introduction to the foundations and recent developments in commutative algebra. A look at the contents of the first five chapters shows that the topics covered are those usually found in any textbook on commutative algebra. However, this book differs significantly from most commutative algebra textbooks: namely in its treatment of the Dedekind?Mertens formula, the (small) finitistic dimension of a ring, Gorenstein rings, valuation overrings, the valuative dimension, and the Nagata rings. Chapter 6 goes on to present w-modules over commutative rings, as they are most commonly used in torsion theory and multiplicative ideal theory. Chapter 7 deals with multiplicative ideal theory over integral domains. Chapter 8 collects various results of pullbacks, especially Milnor squares and D + M constructions, which are probably the most important example-generating machines. In Chapter 9, coherent rings of finite weak global dimensions are probed, and the local ring of weak global dimension two is elaborated by combining homological tricks and methods of star operation theory. Chapter 10 is devoted to the Grothendieck group of a commutative ring. In particular, the Bass?Quillen problem is discussed. Finally, Chapter 11 introduces relative homological algebra, especially where the related notions of integral domains appearing in classical ideal theory are defined and studied using the class of Gorenstein projective modules. In Chapter 12, in this new edition, properties of cotorsion theories are introduced and show, for any cotorsion pair, how to construct their homology theory. Each section of the book is followed by a selection of exercises of varying difficulty. This book appeals to a wide readership, from graduate students to academic researchers interested in studying commutative algebra. 410 0$aAlgebra and Applications,$x2192-2950 ;$v31 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 $a512.44 700 $aWang$b Fanggui$0755915 701 $aKim$b Hwankoo$0755916 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910886090503321 996 $aFoundations of commutative rings and their modules$91523345 997 $aUNINA