The fundamental constituents of iteration digraphs of finite commutative rings

Nan, Jizhu, Wei, Yangjiang, and Tang, Gaohua. "The fundamental constituents of iteration digraphs of finite commutative rings." Czechoslovak Mathematical Journal 64.1 (2014): 199-208. <http://eudml.org/doc/262035>.

@article{Nan2014,
abstract = {For a finite commutative ring $R$ and a positive integer $k\geqslant 2$, we construct an iteration digraph $G(R, k)$ whose vertex set is $R$ and for which there is a directed edge from $a\in R$ to $b\in R$ if $b=a^k$. Let $R=R_1\oplus \ldots \oplus R_s$, where $s>1$ and $R_i$ is a finite commutative local ring for $i\in \lbrace 1, \ldots , s\rbrace $. Let $N$ be a subset of $\lbrace R_1, \dots , R_s\rbrace $ (it is possible that $N$ is the empty set $\emptyset $). We define the fundamental constituents $G_N^*(R, k)$ of $G(R, k)$ induced by the vertices which are of the form $\lbrace (a_1, \dots , a_s)\in R\colon a_i\in \{\rm D\}(R_i)$ if $R_i\in N$, otherwise $a_i\in \{\rm U\}(R_i), i=1,\ldots ,s\rbrace ,$ where U$(R)$ denotes the unit group of $R$ and D$(R)$ denotes the zero-divisor set of $R$. We investigate the structure of $G_N^*(R, k)$ and state some conditions for the trees attached to cycle vertices in distinct fundamental constituents to be isomorphic.},
author = {Nan, Jizhu, Wei, Yangjiang, Tang, Gaohua},
journal = {Czechoslovak Mathematical Journal},
keywords = {iteration digraph; fundamental constituent; digraphs product; iteration digraph; fundamental constituent; digraphs product},
language = {eng},
number = {1},
pages = {199-208},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The fundamental constituents of iteration digraphs of finite commutative rings},
url = {http://eudml.org/doc/262035},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Nan, Jizhu
AU - Wei, Yangjiang
AU - Tang, Gaohua
TI - The fundamental constituents of iteration digraphs of finite commutative rings
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 1
SP - 199
EP - 208
AB - For a finite commutative ring $R$ and a positive integer $k\geqslant 2$, we construct an iteration digraph $G(R, k)$ whose vertex set is $R$ and for which there is a directed edge from $a\in R$ to $b\in R$ if $b=a^k$. Let $R=R_1\oplus \ldots \oplus R_s$, where $s>1$ and $R_i$ is a finite commutative local ring for $i\in \lbrace 1, \ldots , s\rbrace $. Let $N$ be a subset of $\lbrace R_1, \dots , R_s\rbrace $ (it is possible that $N$ is the empty set $\emptyset $). We define the fundamental constituents $G_N^*(R, k)$ of $G(R, k)$ induced by the vertices which are of the form $\lbrace (a_1, \dots , a_s)\in R\colon a_i\in {\rm D}(R_i)$ if $R_i\in N$, otherwise $a_i\in {\rm U}(R_i), i=1,\ldots ,s\rbrace ,$ where U$(R)$ denotes the unit group of $R$ and D$(R)$ denotes the zero-divisor set of $R$. We investigate the structure of $G_N^*(R, k)$ and state some conditions for the trees attached to cycle vertices in distinct fundamental constituents to be isomorphic.
LA - eng
KW - iteration digraph; fundamental constituent; digraphs product; iteration digraph; fundamental constituent; digraphs product
UR - http://eudml.org/doc/262035
ER -