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J. Korean Math. Soc. 2009; 46(2): 313-325
Printed March 1, 2009
Copyright © The Korean Mathematical Society.
Zero-divisor graphs with respect to primal and weakly primal ideals
Shahabaddin Ebrahimi Atani and Ahamd Yousefian Darani
Guilan University and University of Mohaghegh Ardabili
We consider zero-divisor graphs with respect to primal, non-primal, weakly prime and weakly primal ideals of a commutative ring $R$ with non-zero identity. We investigate the interplay between the ring-theoretic properties of $R$ and the graph-theoretic properties of $\Gamma_{I} (R)$ for some ideal $I$ of $R$. Also we show that the zero-divisor graph with respect to primal ideals commutes by localization.
Keywords: zero-divisor graph, primal, weakly primal
MSC numbers: 05C75, 13A15
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