By Graham J. Leuschke
This publication is a accomplished therapy of the illustration conception of maximal Cohen-Macaulay (MCM) modules over neighborhood jewelry. This subject is on the intersection of commutative algebra, singularity conception, and representations of teams and algebras. introductory chapters deal with the Krull-Remak-Schmidt Theorem on forte of direct-sum decompositions and its failure for modules over neighborhood jewelry. Chapters 3-10 learn the imperative challenge of classifying the earrings with purely finitely many indecomposable MCM modules as much as isomorphism, i.e., earrings of finite CM style. the elemental material--ADE/simple singularities, the double branched disguise, Auslander-Reiten thought, and the Brauer-Thrall conjectures--is lined basically and entirely. a lot of the content material hasn't ever sooner than seemed in publication shape. Examples comprise the illustration thought of Artinian pairs and Burban-Drozd's similar building in measurement , an creation to the McKay correspondence from the viewpoint of maximal Cohen-Macaulay modules, Auslander-Buchweitz's MCM approximation thought, and a cautious remedy of nonzero attribute. the rest seven chapters current effects on bounded and countable CM kind and at the illustration thought of completely reflexive modules.
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