On the 2-absorbing ideals and zero divisor graph of equivalence classes op zero divisors

Document Type : Research Paper

Authors

Department of Mathematics, Imam Khomeini International University , P.O.Box 34149-1-6818, Qazvin, Iran

Abstract

Let R be a commutative ring, I be a 2-absorbing ideal of R and let I = Q1 ∩ · · · ∩ Qn (n ≥ 2) with √Qi = Pi for i = 1, · · · , 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 Q1 ∩ · · · ∩ Qn−1, Q1 ∩ · · · ∩ Qn−2, · · · , Q1, P1, P2 · · · , Pn are all vertices of ΓE(R/I) and also the degrees of all vertices are determined. 

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References

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Journal of Hyperstructures
Volume 3, Issue 1
June 2014
Pages 1-9

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