ON QUASI-ZERO DIVISOR GRAPHS OF NON-COMMUTATIVE RINGS

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Amirjan Raziyeh; HASHEMI EBRAHIM

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Journal: Algebraic structures and their applications Year:2018 | Volume:5 | Issue:2 Page(s): 1-13

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Information Journal Paper

Title

ON QUASI-ZERO DIVISOR GRAPHS OF NON-COMMUTATIVE RINGS

Author(s)

Amirjan Raziyeh | HASHEMI EBRAHIM | Issue Writer Certificate

Keywords

quasi-zero-divisor graph

zero-divisor graph

reversible ring

reduced ring

diameter

Abstract

Let R be an associative ring with identity. A ring R is called reversible if ab = 0, then ba = 0 for a; b ∈ R. The quasi-zero-divisor graph of R, denoted by 􀀀 (R) is an undirected graph with all nonzero zero-divisors of R as vertex set and two distinct vertices x and y are adjacent if and only if there exists 0 ̸ = r ∈ R\(ann(x)∪ ann(y)) such that xry = 0 or yrx = 0. In this paper, we determine the diameter and girth of 􀀀 (R). We show that the zero-divisor graph of R denoted by 􀀀 (R), is a spanning subgraph of 􀀀 (R). Also, we investigate when 􀀀 (R) is identical to 􀀀 (R). Moreover, for a reversible ring R, we study the diameter and girth of 􀀀 (R[x]) and we investigate when 􀀀 (R[x]) is identical to 􀀀 (R[x]).

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APA: Copy

Amirjan, Raziyeh, & HASHEMI, EBRAHIM. (2018). ON QUASI-ZERO DIVISOR GRAPHS OF NON-COMMUTATIVE RINGS. ALGEBRAIC STRUCTURES AND THEIR APPLICATIONS, 5(2), 1-13. SID. https://sid.ir/paper/354242/en

Vancouver: Copy

Amirjan Raziyeh, HASHEMI EBRAHIM. ON QUASI-ZERO DIVISOR GRAPHS OF NON-COMMUTATIVE RINGS. ALGEBRAIC STRUCTURES AND THEIR APPLICATIONS[Internet]. 2018;5(2):1-13. Available from: https://sid.ir/paper/354242/en

IEEE: Copy

Raziyeh Amirjan, and EBRAHIM HASHEMI, “ON QUASI-ZERO DIVISOR GRAPHS OF NON-COMMUTATIVE RINGS,” ALGEBRAIC STRUCTURES AND THEIR APPLICATIONS, vol. 5, no. 2, pp. 1–13, 2018, [Online]. Available: https://sid.ir/paper/354242/en

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