In this paper we study the relation between the resolution of Weyl Module F K ) 3 , 4 , 4 (
in
characteristic-free mode and in the Lascoux mode (characteristic zero), more precisely we
obtain the Lascoux resolution of F K ) 3 , 4 , 4 (
in characteristic zero as an application of the
resolution of F K ) 3 , 4 , 4 (
in characteristic-free.
Key word : Resolution, Weyl module, Lascoux mode, divided power, characteristic-free.

In this paper, the complex of Lascoux in the case of partition (3,3,2) has been studied by using diagrams ,divided power of the place polarization ) (k ij ,Capelli identites and the idea of mapping Cone .

In this paper, there are two main objectives. The first objective is to study the relationship between the density property and some modules in detail, for instance; semisimple and divisible modules. The Addition complement has a good relationship with the density property of the modules as this importance is highlighted by any submodule N of M has an addition complement with Rad(M)=0. The second objective is to clarify the relationship between the density property and the essential submodules with some examples. As an example of this relationship, we studied the torsion-free module and its relationship with the essential submodules in module M.

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The launch of the EU’s Eastern Partnership in 2009 intended to signal a new, elevated level of EU engagement with its Eastern neighborhood. Yet there remain several long-simmering and potentially destabilizing conflicts in the region, with which EU engagement thus far has been sporadic at best. The Union’s use of its Common Security and Defense Policy (CSDP) in the region and to help solve these disputes has been particularly ad hoc and inconsistent, wracked by inter-institutional incoherence and undermined by Member States’ inability to agree on a broad strategic vision for engagement with the area.

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