This paper studies connections between the preprojective modules over the path algebra of a finite connected quiver without oriented cycles, the (+)-admissible sequences of vertices, and the Weyl group. For each preprojective module, there exists a unique up to a certain equivalence shortest (+)-admissible sequence annihilating the module. A (+)-admissible sequence is the shortest sequence anni...

Let G be a finite group, k a perfect field, and V a finite dimensional kG-module. We let G act on the power series k[[V ]] by linear substitutions and address the question of when the invariant power series k[[V ]] form a unique factorization domain. We prove that for a permutation module for a p-group in characteristic p, the answer is always positive. On the other hand, if G is a cyclic group...

Given a tournament T, module of T is subset X V(T) such that for x,y?X and v?V(T)?X, (x,v)?A(T) if only (y,v)?A(T). The trivial modules are 0?, {u} (u?V(T)) V(T). indecomposable all its trivial; otherwise it decomposable. decomposability index denoted by ?(T), the smallest number arcs must be reversed to make indecomposable. first author conjectured n?5, we have ?(n)=n+14, where ?(n) maximum ?(...

All rings considered are associative with identity and all occurring modules are unital right modules. We denote by Mod R the category of all R-modules. The spectrum of a ring R is known to be the “set” of isomorphism classes of indecomposable injective right R-modules. When R is right-Noetherian the spectrum describes all injective Rmodules, since each injective module is a direct sum of indec...

R.G. and Perez proved that under certain conditions the test ideal of a module closure agrees with trace closure. We use this fact to compute ideals various rings respect closures coming from their indecomposable maximal Cohen–Macaulay modules. also give an easier way hypersurface ring in three variables particular type matrix factorization.

1.1 Let A = kG, the group algebra of some finite group where the characteristic of the field k divides |G|. In contrast to working over the complex field, the kG-modules are not usually semisimple. If a Sylow p-subgroup of G is not cyclic then there are infinitely many indecomposable kG-modules, and we usually enjoy little control over the category of such modules. It is therefore instructive t...

The aim of this paper is to extend results established by H. Onoand T. Kowalski regarding directly indecomposable commutative residuatedlattices to the non-commutative case. The main theorem states that a residuatedlattice A is directly indecomposable if and only if its Boolean center B(A)is {0, 1}. We also prove that any linearly ordered residuated lattice and anylocal residuated lattice are d...

The modules for a Chevalley group arising from admissible lattices in an irreducible module for the associated complex semisimple Lie algebra are studied. It is proved that the transpose of such a module is still in this collection and generically the cohomology modules of line bundles on the flag varieties are in this collection also. In the rank 1 case, all modules in this collection are inde...

This paper gives a necessary and sufficient condition for the image of Specht module under inverse Schur functor to be isomorphic dual Weyl in characteristic 2, an elementary proof that this isomorphism holds all cases other characteristics. These results are new characteristics 2 3. We deduce some examples indecomposable modules 2. When does not hold, is still quotient module, we prove additio...