The rings considered in this article are commutative with identity which are not integral
domains. Let $ R $ be a ring. An ideal $ I $ of $ R $ is said to be an annihilating ideal of $ R …

The rings considered in this article are commutative with identity which admit at least one
nonzero annihilating ideal. Let RR be such a ring. If Z (R) Z (R), the set of zero-divisors of …

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 …

The rings considered in this paper are commutative with identity which are not integral
domains. Recall that an ideal I of a ring R is called an annihilating ideal if there exists r∈ …

Let R be a commutative non-domain ring with identity and let A (R)∗ denote the set of all
nonzero annihilating ideals of R. Recall that the annihilating-ideal graph of R, denoted by …

The rings considered in this paper are commutative with identity which are not integral
domains. Let R be a ring. Let us denote the set of all annihilating ideals of R by 𝔸 (R) and 𝔸 …

The rings considered in this article are commutative with identity. For an ideal I of a ring R,
we denote the annihilator of I in R by Ann(I). An ideal I of a ring R is said to be an exact …

Let R be a commutative ring with identity which is not an integral domain. An ideal I of a ring
R is called an annihilating ideal if there exists r∈ R\{0} such that I r=(0). Let Ω (R) be a …

Let $ S $ be a semigroup with $0 $ and $ R $ be a ring with $1 $. We extend the definition of
the zero-divisor graphs of commutative semigroups to not necessarily commutative …

Rings considered in this article are commutative with identity which admit at least one
nonzero annihilating ideal. For such a ring R, we determine necessary and sufficient …