The Duality of the Formal Local Homology Together With The Edge Ideal of a Graph

Authors

Carlos Henrique Tognon, Department of Mathematics, Federal University of Vic¸osa, 36570000 - Vic¸osa - MG, BrazilFollow
Catarina Mendes de Jesus, Department of Mathematics, Federal University of Vic¸osa, 36570000 - Vic¸osa - MG, BrazilFollow

Author Country (or Countries)

Brazil

Abstract

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.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/journal/100302

Recommended Citation

Henrique Tognon, Carlos and Mendes de Jesus, Catarina (2018) "The Duality of the Formal Local Homology Together With The Edge Ideal of a Graph," Applied Mathematics & Information Sciences: Vol. 12: Iss. 2, Article 2.
DOI: http://dx.doi.org/10.18576/journal/100302
Available at: https://digitalcommons.aaru.edu.jo/amis/vol12/iss2/2