Turkish Journal of Mathematics
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 $S$.
DOI
10.3906/mat-1503-2
Keywords
Iteration digraph, isomorphic component, isomorphic digraph
First Page
872
Last Page
883
Recommended Citation
WEI, Y, & TANG, G (2015). The iteration digraphs of finite commutative rings. Turkish Journal of Mathematics 39 (6): 872-883. https://doi.org/10.3906/mat-1503-2
