Serial rings and direct decompositions
نویسندگان
چکیده
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...
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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 کاملSerial Rings
A module is called uniseriat if it has a unique composition series of finite length. A ring (always with 1) is called serial if its right and left free modules are direct sums of uniserial modules. Nakayama, who called these rings generalized uniserial rings, proved [21, Theorem 171 that every finitely generated module over a serial ring is a direct sum of uniserial modules. In section one we g...
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 ...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1984
ISSN: 0022-4049
DOI: 10.1016/0022-4049(84)90076-8