On the compressed essential graph of a commutative ring

Let [Formula: see text] be a commutative ring and [Formula: see text] be an [Formula: see text]-module. The compressed essential graph of [Formula: see text], denoted by [Formula: see text] is a simple undirected graph associated to [Formula: see text] whose vertices are classes of torsion elements of [Formula: see text] and two distinct classes [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text] is an essential ideal of [Formula: see text]. In this paper, we study diameter and girth of [Formula: see text] and we characterize all modules for which the compressed essential graph is connected. Moreover, it is proved that [Formula: see text], whenever [Formula: see text] is Noetherian and [Formula: see text] is a finitely generated multiplication module with [Formula: see text].

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On the compressed essential graph of a module over a commutative ring

Payrovi

Babaei

Sevim

2020

Asian-European J. Math.

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On the compressed essential graph of a commutative ring

Cited by 1 publication

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On the compressed essential graph of a module over a commutative ring

On the compressed essential graph of a module over a commutative ring

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