Title of article
THE TOTAL GRAPH OF ANNIHILATING ONE-SIDED IDEALS OF A RING
Author/Authors
Alibemani, Abolfazl Faculty of Mathematical Sciences - Shahrood University of Technology , Hashemi, Ebrahim Faculty of Mathematical Sciences - Shahrood University of Technology , Alhevaz, Abdollah Faculty of Mathematical Sciences - Shahrood University of Technology
Pages
16
From page
61
To page
76
Abstract
Let
R
R be an associative ring with
1
≠
0
1≠0 which is not a domain. Let
A
(
R
)
∗
=
{
I
⊆
R
∣
I
i
s
a
l
e
f
t
o
r
r
i
g
h
t
i
d
e
a
l
o
f
R
a
n
d
l
.
a
n
n
(
I
)
∪
r
.
a
n
n
(
I
)
≠
0
}
∖
{
0
}
A(R)
∗
={I⊆R ∣ I is a left or right ideal of R and l.ann(I)∪r.ann(I)≠0}∖{0}. The total graph of annihilating one-sided ideals of
R
R, denoted by
Ω
(
R
)
Ω(R), is a graph with the vertex set
A
(
R
)
∗
A(R)
∗
and two distinct vertices
I
I and
J
J are adjacent if
l
.
a
n
n
(
I
+
J
)
∪
r
.
a
n
n
(
I
+
J
)
≠
0
l.ann(I+J)∪r.ann(I+J)≠0. In this paper, we study the relations between the graph-theoretic properties of this graph and some algebraic properties of rings. We characterize all rings whose graphs are disconnected. Also, we study diameter, girth, independence number, domination number and planarity of this graph
Keywords
Total graph , diameter , reversible ring , semicommutative ring , skew polynomial ring
Journal title
International Electronic Journal of Algebra
Serial Year
2020
Full Text URL
Record number
2599160
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