Direct decompositions

Singularities 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 ...

Direct Decompositions of Algebraic Systems

Preliminaries. An operator group with a principal series can obviously be written as a direct product of finitely many directly indecomposable admissible subgroups, and the classical WedderburnRemak-Krull-Schmidt theorem asserts that this representation is unique up to isomorphism. Numerous generalizations of this theorem are known in the literature. Thus it follows from the results in Baer [l;...

Direct Product Decompositions of Lattices , Closures andRelation

In this paper we study the direct product decompositions of closure operations and lattices of closed sets. We characterize the direct product decompositions of lattices of closed sets in terms of closure operations, and nd those decompositions of lattices which correspond to the decompositions of closures. If a closure on a nite set is represented by its implication base (i.e. a binary relatio...

Direct Decompositions of Atomistic Algebraic Lattices

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...