Zero-divisor graphs of unitary R-modules over commutative rings. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Aijaz, M.; Pirzada, S.; Somasundaram, A.
• Is Part Of: AKCE International Journal of Graphs and Combinatorics. Volume 19:Issue 1(2022)
• Page Start: 69
• Page End: 73
• Publication Date: 2022-01-02
• Subjects: Module -- ring -- zero divisor graph of module -- complete graph -- diameter -- clique; 13A99 -- 05C12 -- 05C25 -- 05C78
• DOI: 10.1080/09728600.2022.2058895
• Languages: English
• ISSNs: 0972-8600

Abstract

Abstract: Let R be a commutative ring with unity 1 ≠ 0 and let M be a unitary R − module. In this paper, we derive some completeness conditions on the zero divisor graphs of modules over commutative rings. It is shown that the weak zero divisor graph of a simple R − module is complete if and only if R is a field. We investigate the zero divisor graphs in finitely generated R − modules. We find the diameter, the girth, the clique number and the vertex degrees of the zero-divisor graphs of the rings of integer modulo n as Z − modules.