交换环的湮灭理想图的推广

Pub Date : 2020-01-01 DOI:10.4134/CKMS.C200006

Mahtab Koohi Kerahroodi, Fatemeh Nabaei

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引用次数: 0

摘要

设R是一个有单位的交换环。R的湮灭理想图AG(R)的扩展是顶点为R的非零湮灭理想且两个不同的顶点I和J相邻的图，当且仅当n,m∈n使得InJm =(0)与In, Jm 6=(0)。首先，我们区分AG(R)与AG(R)重合的情况。然后，我们刻画了当R是环的有限直积时AG(R)的直径和周长。此外，我们证明了AG(R)包含一个环，如果AG(R) 6= AG(R)。

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AN EXTENSION OF ANNIHILATING-IDEAL GRAPH OF COMMUTATIVE RINGS

Let R be a commutative ring with unity. The extension of annihilating-ideal graph of R, AG(R), is the graph whose vertices are nonzero annihilating ideals of R and two distinct vertices I and J are adjacent if and only if there exist n,m ∈ N such that InJm = (0) with In, Jm 6= (0). First, we differentiate when AG(R) and AG(R) coincide. Then, we have characterized the diameter and the girth of AG(R) when R is a finite direct products of rings. Moreover, we show that AG(R) contains a cycle, if AG(R) 6= AG(R).

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