Turkish Journal of Mathematics
DOI
10.3906/mat-1503-2
Abstract
For a finite commutative ring $S$ (resp., a finite abelian group $S$) and a positive integer $k\geqslant2$, we construct an iteration digraph $G(S, k)$ whose vertex set is $S$ and for which there is a directed edge from $a\in S$ to $b\in S$ if $b=a^k$. We generalize some previous results of the iteration digraphs from the ring $\mathbb{Z}_n$ of integers modulo $n$ to finite commutative rings, and establish a necessary and sufficient condition for $G(S, k_1)$ and $G(S, k_2)$ to be isomorphic for any finite abelian group $S$.
Keywords
Iteration digraph, isomorphic component, isomorphic digraph
First Page
872
Last Page
883
Recommended Citation
WEI, YANGJIANG and TANG, GAOHUA
(2015)
"The iteration digraphs of finite commutative rings,"
Turkish Journal of Mathematics: Vol. 39:
No.
6, Article 8.
https://doi.org/10.3906/mat-1503-2
Available at:
https://journals.tubitak.gov.tr/math/vol39/iss6/8
