By Laszlo Fuchs

This publication offers a accomplished exposition of using set-theoretic tools in abelian crew idea, module concept, and homological algebra, together with purposes to Whitehead's challenge, the constitution of Ext and the lifestyles of almost-free modules over non-perfect jewelry. This moment variation is totally revised and udated to incorporate significant advancements within the decade because the first variation. between those are functions to cotorsion theories and covers, together with an explanation of the Flat hide Conjecture, in addition to using Shelah's pcf conception to constuct virtually unfastened teams. As with the 1st variation, the publication is essentially self-contained, and designed to be obtainable to either graduate scholars and researchers in either algebra and common sense. they'll locate there an creation to robust strategies which they might locate beneficial of their personal paintings Commutative domain names and Their Modules -- Generalities on domain names -- Fractional beliefs -- crucial dependence -- Module different types -- Lemmas on Hom and Ext -- Lemmas on tensor and torsion items -- Divisibility and relative divisibility -- natural submodules -- The trade estate -- Semilocal endomorphism earrings -- Valuation domain names -- primary homes of valuation domain names -- completely ordered abelian teams -- Valuations -- beliefs of valuation domain names -- the category semigroup -- Maximal and nearly maximal valuation domain names -- Henselian valuation earrings -- Strongly discrete valuation domain names -- Prufer domain names -- basic homes and characterizations -- Prufer domain names of finite personality -- the category semigroup -- Lattice-ordered abelian teams -- Bezout domain names -- straight forward divisor domain names -- Strongly discrete Prufer domain names -- extra Non-Noetherian domain names -- Krull domain names -- Coherent domain names -- h-Local domain names -- Matlis domain names -- Reflexive domain names -- Finitely Generated Modules -- Cyclic modules -- Finitely generated modules -- Finitely offered modules -- Finite displays -- Finitely generated modules over valuation domain names -- Indecomposable finitely generated modules -- Finitely generated modules with neighborhood endomorphism jewelry -- Decompositions of finitely generated modules -- Finitely generated modules with no the Krull-Schmidt estate -- domain names whose finitely generated modules are direct sums of cyclics -- Projectivity and Projective size -- Projective modules -- Projective size