| Title:
|
The fundamental constituents of iteration digraphs of finite commutative rings (English) |
| Author:
|
Nan, Jizhu |
| Author:
|
Wei, Yangjiang |
| Author:
|
Tang, Gaohua |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
1 |
| Year:
|
2014 |
| Pages:
|
199-208 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $i\in \{1, \ldots , s\}$. Let $N$ be a subset of $\{R_1, \dots , R_s\}$ (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 $\{(a_1, \dots , a_s)\in R\colon a_i\in {\rm D}(R_i)$ if $R_i\in N$, otherwise $a_i\in {\rm U}(R_i), i=1,\ldots ,s\},$ 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. (English) |
| Keyword:
|
iteration digraph |
| Keyword:
|
fundamental constituent |
| Keyword:
|
digraphs product |
| MSC:
|
05C05 |
| MSC:
|
11A07 |
| MSC:
|
13M05 |
| idZBL:
|
Zbl 06391487 |
| idMR:
|
MR3247455 |
| DOI:
|
10.1007/s10587-014-0094-9 |
| . |
| Date available:
|
2014-09-29T09:52:46Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143960 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
