A triangulated category is said to be indecomposable if it admits no nontrivial semiorthogonal decompositions. We introduce a definition of noncommutatively stably semiorthogonally (NSSI) variety. This propery implies, among other things, that each smooth proper subvariety has derived coherent sheaves, and $Y$ NSSI, then for any variety $X$ all decompositions $X \times Y$ are induced from $X$. ...

We develop a criterion for coalition formation among goal-directed agents, the indecomposable do-ut-des property. The indecomposable do-ut-des property refines the do-ut-des property (literally give to get) by considering the fact that agents prefer to form coalitions whose components cannot be formed independently. A formal description of this property is provided as well as an analysis of alg...

Let R be local Noetherian ring of depth at least two. We prove that there are indecomposable R-modules which are free on the punctured spectrum of constant, arbitrarily large, rank.

Several results about the multiplicities of indecomposable injectives in the minimal injective resolution of a ring exist in the literature. Mostly these apply to universal enveloping algebras of finite dimensional solvable Lie algebras, and to Gorenstein noetherian PI local rings. We unify these results and extend them to the much wider class of rings with Auslander dualizing complexes.

An indecomposable Riemannian symmetric space which admits nontrivial twistor spinors has constant sectional curvature. Furthermore, each homogeneous Riemannian manifold with parallel spinors is at. In the present paper we solve the twistor equation on all indecomposable Lorentzian symmetric spaces explicitly. In particular, we show that there are-in contrast to the Riemannian case-indecom-posab...

In this paper, working over Z(p) and using algebra perturbation results from [18], p-minimal homological models of twisted tensor products (TTPs) of Cartan’s elementary complexes are obtained. Moreover, making use of the notion of indecomposability of a TTP, we deduce that a homological model of a indecomposable p-minimal TTP of length ` (` ≥ 2) of exterior and divided power algebras is a tenso...

A tournament is acyclically indecomposable if no acyclic autonomous set of vertices has more than one element. We identify twelve infinite acyclically indecomposable tournaments and prove that every infinite acyclically indecomposable tournament contains a subtournament isomorphic to one of these tournaments. The profile of a tournament T is the function φT which counts for each integer n the n...

Indecomposable Schur rings over a cyclic group Zn of order n are considered. In the case n = p, p an odd prime, the total number of such rings was described in terms of Catalan numbers by Liskovets and Pöschel [Discr. Math. 214 (2000), 173–191]. Here, a closed formula is shown for the total number of indecomposable Schur rings over Z2m using Catalan and Schröder numbers. The result is obtained ...

For any field F, a polynomial f ∈ F [x1, x2, . . . , xk] can be associated with a polytope, called its Newton polytope. If the polynomial f has integrally indecomposable Newton polytope, in the sense of Minkowski sum, then it is absolutely irreducible over F, i.e., irreducible over every algebraic extension of F.We present some results giving new integrally indecomposable classes of polygons. C...

We discuss irreducible highest weight representations of the sl2 loop algebra and reducible indecomposable ones in association with the sl2 loop algebra symmetry of the six-vertex model at roots of unity. We formulate an elementary proof that every highest weight representation with distinct evaluation parameters is irreducible. We present a general criteria for a highest weight representation ...