ZERO-DIVISOR GRAPHS WITH RESPECT TO PRIMAL AND WEAKLY PRIMAL IDEALS

Title & Authors
ZERO-DIVISOR GRAPHS WITH RESPECT TO PRIMAL AND WEAKLY PRIMAL IDEALS
Atani, Shahabaddin Ebrahimi; Darani, Ahamd Yousefian;

Abstract
We consider zero-divisor graphs with respect to primal, nonprimal, weakly prime and weakly primal ideals of a commutative ring R with non-zero identity. We investigate the interplay between the ringtheoretic properties of R and the graph-theoretic properties of $\small{{\Gamma}_I(R)}$ 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;
Language
English
Cited by
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4.
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