# The regular digraph of ideals of a commutative ring

@article{Nikmehr2012TheRD,
title={The regular digraph of ideals of a commutative ring},
journal={Acta Mathematica Hungarica},
year={2012},
volume={134},
pages={516-528}
}
• Published 1 March 2012
• Mathematics
• Acta Mathematica Hungarica
AbstractLet R be a commutative ring and Max (R) be the set of maximal ideals of R. The regular digraph of ideals of R, denoted by $\overrightarrow{\Gamma_{\mathrm{reg}}}(R)$ , is a digraph whose vertex set is the set of all non-trivial ideals of R and for every two distinct vertices I and J, there is an arc from I to J whenever I contains a J-regular element. The undirected regular (simple) graph of ideals of R, denoted by Γreg(R), has an edge joining I and J whenever either I contains a J…
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