Bulletin of the Australian Mathematical Society, ( ISI ), Volume (88), No (1), Year (2013-4) , Pages (177-189)

Title : ( On the Regular Digraph of Ideals of Commutative Rings )

Authors: M. Afkhami , Masoud Karimi , Kazem Khashyarmanesh ,

Access to full-text not allowed by authors

Citation: BibTeX | EndNote

Let R be a commutative ring. The regular digraph of ideals of R, denoted by T(R), is a digraph whose vertex set is the set of all nontrivial ideals of R and, for every two distinct vertices I and J, there is an arc from I to J whenever I contains a nonzero divisor on J. In this paper, we study the connectedness of T(R). We also completely characterise the diameter of this graph and determine the number of edges in T(R), whenever R is a finite direct product of fields. Among other things, we prove that R has a finite number of ideals if and only if N-T(R)(I) is finite, for all vertices I in T(R), where N-T(R)(I) is the set of all adjacent vertices to I in T(R).

Keywords

, regular digraph, connectedness,
برای دانلود از شناسه و رمز عبور پرتال پویا استفاده کنید.

@article{paperid:1040002,
author = {M. Afkhami and Karimi, Masoud and Khashyarmanesh, Kazem},
title = {On the Regular Digraph of Ideals of Commutative Rings},
journal = {Bulletin of the Australian Mathematical Society},
year = {2013},
volume = {88},
number = {1},
month = {April},
issn = {0004-9727},
pages = {177--189},
numpages = {12},
keywords = {regular digraph; connectedness; diameter},
}

[Download]

%0 Journal Article
%T On the Regular Digraph of Ideals of Commutative Rings
%A M. Afkhami
%A Karimi, Masoud
%A Khashyarmanesh, Kazem
%J Bulletin of the Australian Mathematical Society
%@ 0004-9727
%D 2013

[Download]