Applied Mathematics & Information Sciences

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In this paper, we consider R a commutative ring with identity non-zero and the R-module I(G), which is the edge ideal of a graph simple and finite G, with no isolated vertices. A submodule N of I(G) is called an edge dense submodule if HomR(I(G)/N,ER(I(G))) = 0, where ER(I(G)) is the injective hull of I(G). The R-module I(G) is said to be edge monoform if any nonzero submodule of I(G) is an edge dense submodule. Here in this paper, we presented some results which involve the definition of the module I(G) to be edge monoform.

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