The complement of the 𝑀-intersection graph of ideals of a ring

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Heydari Farideh

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2021 | Volume:6 | Issue:28 Page(s): 17-22

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Title

The complement of the 𝑀-intersection graph of ideals of a ring

Author(s)

Heydari Farideh | Issue Writer Certificate

Keywords

Diameter

Girth

Weakly perfect

Multiplication module

Abstract

Let 𝑅 be a commutative ring with identity and 𝑀 be a unitary 𝑅-module, and let 𝐼 (𝑅 )* be the set of all nontrivial ideals of 𝑅 . The complement of the 𝑀-intersection graph of ideals of 𝑅 , denoted by Γ (𝑅 ), is a graph with the vertex set 𝐼 (𝑅 )*, and two distinct vertices 𝐼 and 𝐽 are adjacent if and only if 𝐼 𝑀 ∩ 𝐽 𝑀 ={0}. In this paper, for every multiplication 𝑅-module 𝑀 , the Diameter and the Girth of Γ (𝑅 ) are determined. Also, we show that if 𝑚 , 𝑛 >1 are two integers and ℤ 𝑛 is a ℤ 𝑚-module, then the complement of the ℤ 𝑛-intersection graph of ideals of ℤ 𝑚 is Weakly perfect.

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APA: Copy

Heydari, Farideh. (2021). The complement of the 𝑀-intersection graph of ideals of a ring. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 6(28 ), 17-22. SID. https://sid.ir/paper/953694/en

Vancouver: Copy

Heydari Farideh. The complement of the 𝑀-intersection graph of ideals of a ring. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2021;6(28 ):17-22. Available from: https://sid.ir/paper/953694/en

IEEE: Copy

Farideh Heydari, “The complement of the 𝑀-intersection graph of ideals of a ring,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 6, no. 28 , pp. 17–22, 2021, [Online]. Available: https://sid.ir/paper/953694/en

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