University of Guilan Journal of Algebra and Related Topics 2345-3931 2026 01 25 Some properties of the edge ideal of a simple graph in the theory of local cohomology modules 9383 10.22124/jart.2025.30655.1800 EN Carlos Henrique Tognon Federal University of Triangulo Mineiro, Brazil Journal Article 2025 06 02 In this paper, we have $R$ a commutative Noetherian ring, with nonzero identity, and $\mathfrak{a}$ an ideal of $R$. Here, we give some results of the theory of modules for local cohomology involving the edge ideal. We introduce the concept of $\mathfrak{a}$-edge minimax $R$-modules and also the concept of $\mathfrak{a}$-edge cominimax $R$-modules, together with the edge ideal of a simple and finite graph, with no isolated vertices. We put results involving these new concepts and present relationships that exist between them. Edge Goldie dimension $\mathfrak{a}$-edge minimax modules $\mathfrak{a}$-edge cominimax modules local cohomology Edge ideal of a graph https://jart.guilan.ac.ir/article_9383_b22cf94cf0df5eadc506c38f4d4e6ae4.pdf