# 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…
20 Citations
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Acta mathematica Hungarica
Acta Mathematica Hungarica features papers covering most areas of mathematics and, in particular, from those whose work is related to the advances being made by Hungarian mathematicians. It publishes