TY - JOUR ID - 765 TI - When does the complement of the annihilating-ideal graph of a commutative ring admit a cut vertex? JO - Algebraic Structures and Their Applications JA - AS LA - en SN - 2382-9761 AU - VISWESWARAN, S. AU - PARMAR, A. AD - Saurashtra University, Rajkot, India Y1 - 2015 PY - 2015 VL - 2 IS - 2 SP - 9 EP - 22 KW - N-prime of $(0)$ KW - B-prime of $(0)$ KW - complement of the annihilating-ideal graph of a commutative ring KW - vertex cut and cut vertex of a connected graph DO - N2 -  The rings considered in this article are  commutative  with identity which admit at least two  nonzero annihilating ideals. Let $R$ be a ring. Let $\mathbb{A}(R)$ denote the set of all annihilating ideals of $R$ and let $\mathbb{A}(R)^{*} = \mathbb{A}(R)\backslash \{(0)\}$. The annihilating-ideal graph of $R$, denoted by $\mathbb{AG}(R)$  is an undirected simple graph whose vertex set is $\mathbb{A}(R)^{*}$ and distinct vertices $I, J$ are joined by an edge in this graph if and only if $IJ = (0)$. The aim of this article is to classify rings  $R$ such that $(\mathbb{AG}(R))^{c}$ ( that is,  the complement of $\mathbb{AG}(R)$)   is connected and admits a cut vertex. UR - https://as.yazd.ac.ir/article_765.html L1 - https://as.yazd.ac.ir/article_765_b8befa609c45c0b6b6a79bc456253b4a.pdf ER -