On a New Extension of the Zero-Divisor Graph

• 作者: A.Cherrabi H.Essannouni E.Jabbouri A.Ouadfel
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2020,（3）
• 页码范围: 469-476
• 页数: 8页
• 语种: 英文
• DOI: 10.1142/S1005386720000383

摘要

In this paper,we introduce a new graph whose vertices are the non-zero zero-divisors of a commutative ring R,and for distincts elements x and y in the set Z(R)* of the non-zero zero-divisors of R,x and y are adjacent if and only if xy =0 or x +y ∈ Z(R).We present some properties and examples of this graph,and we study its relationship with the zero-divisor graph and with a subgraph of the total graph of a commutative ring.