イデアルによるある零因子グラフと数学教育
URI | http://harp.lib.hiroshima-u.ac.jp/it-hiroshima/metadata/9789 | ||||||||||||
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ファイル |
kiyo10027.pdf
( 1025.0 KB )
公開日
:2012-01-31
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タイトル |
イデアルによるある零因子グラフと数学教育
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別タイトル |
Zero divisor graphs by an ideal and mathematical education
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著者 |
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キーワード |
ideal
zero divisor
zero-divisor graph
Euler function
residue class ring
Hasse diagram
2-matching
triangle
4-cycle
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抄録 |
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. |
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掲載雑誌名 |
広島工業大学紀要. 教育編
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巻 |
10
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開始ページ |
27
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終了ページ |
30
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出版年月日 |
2011
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出版者 |
広島工業大学
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ISSN |
1346-9983
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NCID |
AA11599121
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NAID |
40018724504
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本文言語 |
日本語
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資料タイプ |
紀要論文
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著者版フラグ |
出版社版
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旧URI | |||||||||||||
区分 |
it-hiroshima
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