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## 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

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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

On the mathematics education related to the ideal-based zero divisor graphs

氏名 神田 隆至 カンダ タカシ Kanda Takashi
氏名 金光 三男 カネミツ ミツオ Kanemitsu Mitsuo
キーワード
ideal
zero divisor
zero-divisor graph
residue class ring
Hasse diagram
ideal-based zerodivisor graph
mathematics education

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.

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21

2012-02

ISSN
1346-9983
NCID
AA11599121
NAID
40019184004

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