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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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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
Title Alternative
On the mathematics education related to the ideal-based zero divisor graphs
Author
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
Subject
ideal
zero divisor
zero-divisor graph
residue class ring
Hasse diagram
ideal-based zerodivisor graph
mathematics education
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.

Journal Title

Volume
11
Spage
17
Epage
21
Published Date
2012-02
Publisher

ISSN
1346-9983
NCID
AA11599121
NAID
40019184004
Language
jpn
NIIType
Departmental Bulletin Paper
Text Version

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it-hiroshima