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On the 2-absorbing ideals and zero divisor graph of equivalence classes op zero divisors | ||
| Journal of Hyperstructures | ||
| دوره 3، شماره 1، شهریور 2014، صفحه 1-9 اصل مقاله (284.06 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2014.2558 | ||
| نویسندگان | ||
| Sh. Payrovi* ؛ S. Babaei | ||
| Department of Mathematics, Imam Khomeini International University , P.O.Box 34149-1-6818, Qazvin, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| 2-absorbing ideal؛ zero divisor graph | ||
| مراجع | ||
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[1] D. F. Anderson and A. Badawi, On n-absorbing ideals of commutavie rings,Comm. Algebra, 39 (2011), 1646-1672. [2] D. F. Anderson and P. S. Livingston, The zero divisor graph of a commutative ring , J. Algebra, 217 (1999), 434-447. [3] A. Badawi, On 2-absorbing ideals of commutavie rings, Bull. Austral. Math. Soc.,75 (2007), 417-429. [4] I. Beck, Coloring of commutavie rings, J. Algebra, 116 (1988), 208-226. [5] Sh. Payrovi and S. Babaei,On the 2-absorbing ideals in comutative rings,Bull.Malaysian Math.Sci.Soc.23(2013),1511-1526. [6] Shane P. Redmond, An Ideal-Based Zero-Divisor Graph of a Commutative Ring, Comm. Algebra, 31 (2003), 4425-4443. [7] R.Y. Sharp, Steps in commutative algebra, Cambridge: Cambridge University Press. [8] S. Spiroff and C. Wickham, A zero divisor graph determined by equivalence classes of zero divisors, Comm. Algebra, 39 (2011), 2338-2348. | ||
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