دانلود کتاب Modules over non-Noetherian domains

This book provides a comprehensive exposition of the use of set-theoretic methods in abelian group theory, module theory, and homological algebra, including applications to Whitehead's Problem, the structure of Ext and the existence of almost-free modules over non-perfect rings. This second edition is completely revised and udated to include major developments in the decade since the first edition. Among these are applications to cotorsion theories and covers, including a proof of the Flat Cover Conjecture, as well as the use of Shelah's pcf theory to constuct almost free groups. As with the first edition, the book is largely self-contained, and designed to be accessible to both graduate students and researchers in both algebra and logic. They will find there an introduction to powerful techniques which they may find useful in their own work Commutative Domains and Their Modules -- Generalities on domains -- Fractional ideals -- Integral dependence -- Module categories -- Lemmas on Hom and Ext -- Lemmas on tensor and torsion products -- Divisibility and relative divisibility -- Pure submodules -- The exchange property -- Semilocal endomorphism rings -- Valuation Domains -- Fundamental properties of valuation domains -- Totally ordered abelian groups -- Valuations -- Ideals of valuation domains -- The class semigroup -- Maximal and almost maximal valuation domains -- Henselian valuation rings -- Strongly discrete valuation domains -- Prufer Domains -- Fundamental properties and characterizations -- Prufer domains of finite character -- The class semigroup -- Lattice-ordered abelian groups -- Bezout domains -- Elementary divisor domains -- Strongly discrete Prufer domains -- More Non-Noetherian Domains -- Krull domains -- Coherent domains -- h-Local domains -- Matlis domains -- Reflexive domains -- Finitely Generated Modules -- Cyclic modules -- Finitely generated modules -- Finitely presented modules -- Finite presentations -- Finitely generated modules over valuation domains -- Indecomposable finitely generated modules -- Finitely generated modules with local endomorphism rings -- Decompositions of finitely generated modules -- Finitely generated modules without the Krull-Schmidt property -- Domains whose finitely generated modules are direct sums of cyclics -- Projectivity and Projective Dimension -- Projective modules -- Projective dimension