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2. Some results on the annihilator graph of a commutative ring

Creator:
Afkhami, Mojgan, Khashyarmanesh, Kazem, and Rajabi, Zohreh
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, kruhový graf, číslo kliky, chromatická čísla, annihilator graph, zero-divisor graph, outerplanar, ring-graph, cut-vertex, clique number, weakly perfect, chromatic numbers, polynomial ring, ring of fractions, 13, and 51
Language:
English
Description:
Let R be a commutative ring. The annihilator graph of R, denoted by AG(R), is the 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 ann(xy) \neqann R(x)\cup annR(y), where for z \in R, annR(z) = {r \in R: rz = 0}. In this paper, we characterize all finite commutative rings R with planar or outerplanar or ring-graph annihilator graphs. We characterize all finite commutative rings R whose annihilator graphs have clique number 1, 2 or 3. Also, we investigate some properties of the annihilator graph under the extension of R to polynomial rings and rings of fractions. For instance, we show that the graphs AG(R) and AG(T(R)) are isomorphic, where T(R) is the total quotient ring of R. Moreover, we investigate some properties of the annihilator graph of the ring of integers modulo n, where n>1., Mojgan Afkhami, Kazem Khashyarmanesh, Zohreh Rajabi., and Obsahuje bibliografii
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public