منابع مشابه
Direct-sum Decompositions over Local Rings
Let (R,m) be a local ring (commutative and Noetherian). If R is complete (or, more generally, Henselian), one has the Krull-Schmidt uniqueness theorem for direct sums of indecomposable finitely generated R-modules. By passing to the m-adic completion b R, we can get a measure of how badly the Krull-Schmidt theorem can fail for a more general local ring. We assign to each finitely generated R-mo...
متن کاملDirect-sum decompositions over one-dimensional Cohen-Macaulay local rings
1 Alberto Facchini, Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Belzoni 7, I-35131 Padova, Italy, [email protected] 2 Wolfgang Hassler, Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Heinrichstraße 36/IV, A-8010 Graz, Austria, [email protected] 3 Lee Klingler, Department of Mathematical Sciences, Florida Atlanti...
متن کاملDirect-sum decompositions of modules with semilocal endomorphism rings
Let R be a ring and C a class of right R-modules closed under finite direct sums. If we suppose that C has a set of representatives, that is, a set V(C) ⊆ C such that every M ∈ C is isomorphic to a unique element [M ] ∈ V(C), then we can view V(C) as a monoid, with the monoid operation [M1] + [M2] = [M1 ⊕M2]. Recent developments in the theory of commutative monoids (e.g., [4], [15]) suggest tha...
متن کاملSingularities and Direct-sum Decompositions
Let (R; m;k) be a local ring (commutative and Noetherian). We will discuss existence and uniqueness of direct-sum decompositions of nitely generated R-modules. One says that R has nite CM type provided there are only nitely many indecomposable maximal Cohen-Macaulay R-modules up to isomorphism. Among complete equicharacteristic hypersurface rings with k algebraically closed of characteristic 6 ...
متن کاملDirect Sum Cancellation for Modules over One-dimensional Rings
Let R be a one-dimensional Noetherian domain with finite normalization R. In the eighties the second-named author and S. Wiegand developed a mechanism for studying the cancellation problem for finitely generated torsion-free R-modules. The key idea, described in [Wie84] and [WW87], is to represent a given torsion-free module M as a pullback: M −→ RM ↓ ↓ M/fM −→ RM/fM ∗This research was initiate...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2001
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8657