00732nam0 22002533i 450 99626044360331620180629121801.0978110706974920171107d2016----||||0itac50 baengGBRethinking Roman alliancea study in poetics and societyBill GladhillCambridgeNew YorkCambridge University Press2016X, 216 p.24 cmLetteratura latinaBNCF970.9GLADHILL,Bill752089ITsalbcISBD996260443603316V.3.B. 696264479 L.M.V.3.B.413889BKUMARethinking Roman alliance1512035UNISA04058nam 22005775 450 991088609050332120250415004657.0981-9752-84-110.1007/978-981-97-5284-3(MiAaPQ)EBC31642115(Au-PeEL)EBL31642115(CKB)34775346900041(MiAaPQ)EBC31643258(Au-PeEL)EBL31643258(DE-He213)978-981-97-5284-3(EXLCZ)993477534690004120240903d2024 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierFoundations of Commutative Rings and Their Modules /by Fanggui Wang, Hwankoo Kim2nd ed. 2024.Singapore :Springer Nature Singapore :Imprint: Springer,2024.1 online resource (862 pages)Algebra and Applications,2192-2950 ;31981-9752-83-3 Basic 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.This 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.Algebra and Applications,2192-2950 ;31Commutative algebraCommutative ringsAlgebra, HomologicalCommutative Rings and AlgebrasCategory Theory, Homological AlgebraCommutative algebra.Commutative rings.Algebra, Homological.Commutative Rings and Algebras.Category Theory, Homological Algebra.512.44Wang Fanggui755915Kim Hwankoo755916MiAaPQMiAaPQMiAaPQBOOK9910886090503321Foundations of commutative rings and their modules1523345UNINA