On the ۲-absorbing ideals and zero divisor graph of equivalence classes op zero divisors

Let R be a commutative ring, I be a ۲-absorbing ideal of R and let I = Q۱ ∩ · · · ∩ Qn (n ≥ ۲) with √Qi = Pi for i = ۱, · · · , n, be a minimal primary decomposition of I. Let ΓE(R/I) denote the graph of equivalence classes of zero divisors of R/I. It is shown that Q۱ ∩ · · · ∩ Qn−۱, Q۱ ∩ · · · ∩ Qn−۲, · · · , Q۱, P۱, P۲ · · · , Pn are all vertices of ΓE(R/I) and also the degrees of all vertices are determined.

Keywords:

۲-absorbing ideal , zero divisor graph