Swingle [7]1 has given the following definitions. (1) A continuum M is said to be the finished sum of the continua of a collection G if G* = M and no continuum of G is a subset of the sum of the others.2 (2) If » is a positive integer, the continuum M is said to be indecomposable under index » if If is the finished sum of « continua and is not the finished sum of »+1 continua. Swingle has shown...

Critical indecomposable codes were introduced by Assmus [1], who also gave a recursive construction for these objects. One of the key ingredients in the construction is an auxiliary code, which is an indecomposable code of minimum distance at least 3. In terms of actually being able to construct all critical indecomposable codes, however, Assmus leaves many unanswered questions about these auxi...

For the category of group codes, that generalizes the category of linear codes over a finite field, and with the generalized notions of direct sums and indecomposable group codes, we prove that every MDS non trivial code, every perfect non trivial code, and every constant weight nondegenerate group code are indecomposable. We prove that every group code is a direct sum of indecomposable group c...

Given a tournament T = (V, A), with each subset X of V is associated the subtournament T [X] = (X, A∩(X×X)) of T induced by X. A subset I of V is an interval of T provided that for any a, b ∈ I and x ∈ V \I, (a, x) ∈ A if and only if (b, x) ∈ A. For example, ∅, {x}, where x ∈ V , and V are intervals of T called trivial. A tournament is indecomposable if all its intervals are trivial; otherwise,...

Beimel, Tassa and Weinreb (2008) and Farras and Padro (2010) partially characterized access structures of ideal weighted threshold secret sharing schemes in terms of the operation of composition. They classified indecomposable ideal weighted threshold access structures, and proved that any other ideal weighted threshold access structure is a composition of indecomposable ones. It remained uncle...

It is well-known that any semiperfect A ring has a decomposition as a direct sum (product) of indecomposable subrings A = A1 ⊕ · · · ⊕ An such that the Ai-Mod are indecomposable module categories. Similarly any coalgebra C over a field can be written as a direct sum of indecomposable subcoalgebras C = ⊕ I Ci such that the categories of Ci-comodules are indecomposable. In this paper a decomposit...

This research began as an effort to determine exactly which one-dimensional local rings have indecomposable finitely generated modules of arbitrarily large constant rank. The approach, which uses a new construction of indecomposable modules via the bimodule structure on certain Ext groups, turned out to be effective mainly for hypersurface singularities. The argument was eventually replaced by ...