We address some questions concerning indecomposable polynomials and their behaviour under specialization. For instance we give a bound on a prime p for the reduction modulo p of an indecomposable polynomial P (x) ∈ Z[x] to remain indecomposable. We also obtain a Hilbert like result for indecomposability: if f(t1, . . . , tr, x) is an indecomposable polynomial in several variables with coefficie...

We describe a method for an explicit determination of indecomposable preprojective and preinjective representations for extended Dynkin quivers Γ over an arbitrary field K by vector spaces and matrices. This method uses tilting theory and the explicit knowledge of indecomposable modules over the corresponding canonical algebra of domestic type. Further, if K is algebraically closed we obtain al...

(1) If there is an indecomposable representation of dimension v, then v is a root. (2) If v is a real root, then there is a unique (up to an isomorphism) indecomposable representation of dimension v. (3) If v is primitive (meaning that GCD(vi) = 1) and there is an indecomposable representation of dimension v, then pv, the number of parameters for the isomorphism classes of indecomposable repres...

T. Shudo and H. Miyamito [3] showed that C can be decomposed into a direct sum of its indecomposable subcoalgebras of C. Y.H. Xu [5] showed that the decomposition was unique. He also showed that M can uniquely be decomposed into a direct sum of the weak-closed indecomposable subcomodules of M(we call the decomposition the weak-closed indecomposable decomposition ) in [6]. In this paper, we give...

The space of summands (with respect to vector addition) of a convex polytope in n dimensions is studied. This space is shown to be isomorphic to a convex pointed cone in Euclidean space. The extreme rays of this cone correspond to similarity classes of indecomposable polytopes. The decomposition of a polytope is described and a bound is given for the number of indecomposable summands needed. A ...

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...

Pseudo-BL algebras are noncommutative generalizations of BL-algebras and they include pseudo-MV algebras, a class of structures that are categorically equivalent to l-groups with strong unit. In this paper we characterize directly indecomposable pseudo-BL algebras and we define and study different classes of these structures: local, good, perfect, peculiar, and (strongly) bipartite pseudo-BL al...

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...