Abstract
We associate a graph Γ+(R) to a ring R whose vertices are nonzero proper right ideals of R and two vertices I and J are adjacent if I+J=R. Then we try to translate properties of this graph into algebraic properties of R and vice versa. For example, we characterize rings R for which Γ+(R) respectively is connected, complete, planar, complemented or a forest. Also we find the dominating number of Γ+(R).
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Amini, A., Amini, B., Momtahan, E. et al. On a graph of ideals. Acta Math Hung 134, 369–384 (2012). https://doi.org/10.1007/s10474-011-0121-3
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DOI: https://doi.org/10.1007/s10474-011-0121-3
Keywords
- graph of ideals
- planarity
- complete graph
- dominating number
- clique number
- chromatic number
- rings of continuous functions