イデアルによる零因子グラフに関連する数学教育について

概要

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Let R be a commutative ring and I be an ideal of R. By S.P. Redmond, the ideal-based zero-divisor graph ΓI(R) is defined by the following statement: the vertices set is a set {x¬ ∈ R − I | xy ∈¬ I for some y ∈ ¬R − I} and the edges set is a set {[x, y]} where [x, y] is an edge such that xy ∈ I for distinct two vertices x and y. Let R = Zn when Z is the integers and (n) is an ideal of Z generated by n. We consider the ideal-based graphs ΓI(Zn) for n = 1, 2, …, 20. In particular, we treat the case that n = pq and p2 where p and q are distinct prime numbers. This graph is easily understand by students. We use the educational diagrams. These results are useful to students.
広島工業大学の論文