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
URI | http://harp.lib.hiroshima-u.ac.jp/it-hiroshima/metadata/10693 | ||||||||||||
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File |
kiyo11017.pdf
( 805.0 KB )
Open Date
:2012-11-10
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Title |
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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Title Alternative |
On the mathematics education related to the ideal-based zero divisor graphs
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Author |
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Subject |
ideal
zero divisor
zero-divisor graph
residue class ring
Hasse diagram
ideal-based zerodivisor graph
mathematics education
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Abstract |
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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Journal Title |
広島工業大学紀要. 教育編
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Volume |
11
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Spage |
17
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Epage |
21
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Published Date |
2012-02
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Publisher |
広島工業大学
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ISSN |
1346-9983
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NCID |
AA11599121
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NAID |
40019184004
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Language |
jpn
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NIIType |
Departmental Bulletin Paper
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Text Version |
出版社版
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Old URI | |||||||||||||
Set |
it-hiroshima
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