Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2014-03-01

Journal: CZECHOSLOVAK MATHEMATICAL JOURNAL

Included Journals: SCIE

Volume: 64

Issue: 1

Page Number: 199-208

ISSN: 0011-4642

Key Words: iteration digraph; fundamental constituent; digraphs product

Abstract: For a finite commutative ring R and a positive integer k a (c) 1/2 2, we construct an iteration digraph G(R, k) whose vertex set is R and for which there is a directed edge from a a R to b a R if b = a (k) . Let R = R (1) aS center dot aEuro broken vertical bar aS center dot R (s) , where s > 1 and R (i) is a finite commutative local ring for i a {1, aEuro broken vertical bar, s}. Let N be a subset of {R (1), aEuro broken vertical bar, R (s) } (it is possible that N is the empty set ). We define the fundamental constituents G (N) (*) (R, k) of G(R, k) induced by the vertices which are of the form {(a (1), aEuro broken vertical bar, a (s) ) a R: a (i) a D(R (i) ) if R (i) a N, otherwise a (i) a U(R (i) ), i = 1, aEuro broken vertical bar, 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.