| Title:
|
Some results on the co-intersection graph of submodules of a module (English) |
| Author:
|
Mahdavi, Lotf Ali |
| Author:
|
Talebi, Yahya |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
59 |
| Issue:
|
1 |
| Year:
|
2018 |
| Pages:
|
15-24 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be a ring with identity and $M$ be a unitary left $R$-module. The co-intersection graph of proper submodules of $M$, denoted by $\Omega(M)$, is an undirected simple graph whose vertex set $V(\Omega)$ is a set of all nontrivial submodules of $M$ and two distinct vertices $N$ and $K$ are adjacent if and only if $N+K\neq M$. We study the connectivity, the core and the clique number of $\Omega(M)$. Also, we provide some conditions on the module $M$, under which the clique number of $\Omega(M)$ is infinite and $\Omega(M)$ is a planar graph. Moreover, we give several examples for which $n$ the graph $\Omega(\mathbb{Z}_{n})$ is connected, bipartite and planar. (English) |
| Keyword:
|
co-intersection graph |
| Keyword:
|
core |
| Keyword:
|
clique number |
| Keyword:
|
planarity |
| MSC:
|
05C15 |
| MSC:
|
05C25 |
| MSC:
|
05C69 |
| MSC:
|
16D10 |
| idZBL:
|
Zbl 06890393 |
| idMR:
|
MR3783805 |
| DOI:
|
10.14712/1213-7243.2015.230 |
| . |
| Date available:
|
2018-04-17T13:39:45Z |
| Last updated:
|
2020-04-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147175 |
| . |
| Reference:
|
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| . |
