Planar of Special Idealization Rings

Author:

Al-Labadi Manal1,Almuhur Eman Mohammad2

Affiliation:

1. Eman Mohammad Almuhur, Department of Mathematics, University of Petra, Amman, JORDAN, also with Department of Mathematics,Faculty of Basic Sciences and Humanities,Applied Science Private University,Amman, Jordan

2. Department of Mathematics,Faculty of Basic Sciences and Humanities,Applied Science Private University,Amman, Jordan

Abstract

Let R(+)N be the idealization of the ring R by the R-module N. In this paper, we investigate when Γ(R(+)N) is a Planar graph where R is an integral domain and we investigate when Γ(Zn(+)Zm) is a Planar graph.

Publisher

World Scientific and Engineering Academy and Society (WSEAS)

Subject

General Mathematics

Reference9 articles.

1. M. Allabadi M., Futher results on the diameter of zero-divisor graphs of some special idealizations,International Journal of Algebra, Vol. 12 (2010), pp. 609-614.

2. M. Allabadi, On the Diameter of Zero-Divisor Graphs of Idealizations with Respect to Integral Domain,Jordan Journal of Mathematics and Statistics, Vol. 3 (2010), pp. 127-131.

3. D. D. Anderson, M. Naseer, Beck’s coloring of a commutative ring, J. Algebra, Vol.159 (1993), pp. 500-514.

4. D. F. Anderson, P. S. Livingston, The zero-divisor graph of a commutative, J. Algebra, Vol. 217 (1999), pp. 434-447.

5. M. Axtell, J. Stickle, The zero-divisor graph of a commutative rings, textit Journal of Pure and Applied Algebra, Vol.204 (2006), pp. 235-243.

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