The Compressed Annihilator Graph of a Commutative Ring

Sh. Payrovi () and S. Babaei ()
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Sh. Payrovi: Imam Khomeini International University
S. Babaei: Imam Khomeini International University

Indian Journal of Pure and Applied Mathematics, 2018, vol. 49, issue 1, 177-186

Abstract: Abstract Let R be a commutative ring. In this paper, we introduce and study the compressed annihilator graph of R. The compressed annihilator graph of R is the graph AGE(R), whose vertices are equivalence classes of zero-divisors of R and two distinct vertices [x] and [y] are adjacent if and only if ann(x)∪ann(y) ⊂ ann(xy). For a reduced ring R, we show that compressed annihilator graph of R is identical to the compressed zero-divisor graph of R if and only if 0 is a 2-absorbing ideal of R. As a consequence, we show that an Artinian ring R is either local or reduced whenever 0 is a 2-absorbing ideal of R.

Keywords: Annihilator graph; compressed annihilator graph; zero divisor graph; 2-Absorbing ideal (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13226-018-0261-z

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