Applied Mathematics & Information Sciences

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In this paper, is discuted about the formal local homology module and the formal local cohomology module, this last which is the dual of the formal local homology module. For the definition of this two modules are used the definitions of the local cohomology module with respect to an ideal and of the local homology module with respect to an ideal, where this modules are mencioned in the text. Also are put some connection between the formal local cohomology module and the formal local homology module, using some results of the theory of commutative algebra. Moreover, we involve the theory of graphs within of such modules achieving some applications for the edge ideal of a graph.

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