Indecomposable Cohen-Macaulay modules and irreducible maps

Dorin Popescu and Marko Roczen
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Dorin Popescu: INCREST, Dept. of Math.
Marko Roczen: Humboldt-Universität, Sekt. Mathematik

A chapter in Algebraic Geometry, 1990, pp 277-294 from Springer

Abstract: Abstract Let (R, m) be a local CM-ring and M a finitely generated (shortly f.g.) R-module. M is a maximal CM module (shortly MCM R-modules. The isomorphism classes of indecomposable MCM R-modules form the vertices of the Auslander-Reiter quiver Γ(R) of R. Section 3 studies the behaviour of Γ(R) under base change; best results (cf. (3.10), (3.14)) being partial answers to the conjectures from [Sc] (7.3). Unfortunately, the proofs use the difficult theory of Artin approximation (cf. [Ar], or [Pol]).

Keywords: Local Ring; Isomorphism Class; Noetherian Ring; Springer Lecture Note; Split Sequence (search for similar items in EconPapers)
Date: 1990
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DOI: 10.1007/978-94-009-0685-3_14

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