Investigates essentiality graphs for R-modules and their relationships to module properties.
Let R be an associative ring with identity. In this paper weassociate to every R-module M a simple graph Γₑ(M), which we call it the essentiality graph of M. The vertices of Γₑ(M) are nonzero submodules of M and two distinctvertices K and L are considered to be adjacent if and onlyif K∩ L is an essential submodule of $K+L$.We investigate the relationship between some module theoreticproperties of M such as minimality and closedness ofsubmodules with some graph theoretic properties ofΓₑ(M). In general, this graph is not connected. Westudy some special cases in which Γₑ(M) iscomplete or a union of complete connected components and give some examples illustrating each specific case.
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Dorcheh et al. (2023) studied this question.
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