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## イデアルによるある零因子グラフと数学教育

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イデアルによるある零因子グラフと数学教育

Zero divisor graphs by an ideal and mathematical education

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
Euler function
residue class ring
Hasse diagram
2-matching
triangle
4-cycle

Let R be a commutative ring and 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 = Z18 when Z is the integers and (18) is an ideal of Z generated by 18. This graph is easily understood by students. The coefficients of a characteristic polynomial are related to triangles, 4 cycles and 2-matchings. We use the educational diagrams. These results are useful to students.

10

27

30

2011

ISSN
1346-9983
NCID
AA11599121
NAID
40018724504

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