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
File
Title
イデアルによるある零因子グラフと数学教育
Title Alternative
Zero divisor graphs by an ideal and mathematical education
Author
氏名 神田 隆至
ヨミ カンダ タカシ
別名 Kanda Takashi
氏名 金光 三男
ヨミ カネミツ ミツオ
別名 Kanemitsu Mitsuo
Subject
ideal
zero divisor
zero-divisor graph
Euler function
residue class ring
Hasse diagram
2-matching
triangle
4-cycle
Abstract

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.

Journal Title
広島工業大学紀要. 教育編
Volume
10
Spage
27
Epage
30
Published Date
2011
Publisher
広島工業大学
ISSN
1346-9983
NCID
AA11599121
NAID
40018724504
Language
jpn
NIIType
Departmental Bulletin Paper
Text Version
出版社版
Old URI
Set
it-hiroshima