2022/12/25 by Praveen Mathil, Mathil, Praveen, Barkha Baloda +3
Mathematics · #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2212.12900
Let R be a ring with unity. The cozero-divisor graph of a ring R is an undirected simple graph whose vertices are the set of all non-zero and non-unit elements of R and two distinct vertices x and y are adjacent if and only if x ∉ Ry and y ∉ Rx. The reduced cozero-divisor graph of a ring R, is an undirected simple graph whose vertex set is the set of all nontrivial principal ideals of R and two distinct vertices (a) and (b) are adjacent if and only if (a) \not⊂ (b) and (b) \not⊂ (a). In this paper, we characterize all classes of finite non-local commutative rings for which the cozero-divisor graph and reduced cozero-divisor graph is of genus two.