| Title:
|
Comaximal graph of $C(X)$ (English) |
| Author:
|
Badie, Mehdi |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
57 |
| Issue:
|
3 |
| Year:
|
2016 |
| Pages:
|
353-364 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this article we study the comaximal graph $\Gamma'_{_2}C(X)$ of the ring $C(X)$. We have tried to associate the graph properties of $\Gamma'_{_2}C(X)$, the ring properties of $C(X)$ and the topological properties of $X$. Radius, girth, dominating number and clique number of the $\Gamma'_{_2}C(X)$ are investigated. We have shown that $2\leq \operatorname{Rad}\Gamma'_{_2}C(X) \leq 3$ and if $|X|> 2$ then $\mathrm{girth } \Gamma'_{_2}C(X)= 3$. We give some topological properties of $X$ equivalent to graph properties of $\Gamma'_{_2}C(X)$. Finally we have proved that $X$ is an almost $P$-space which does not have isolated points if and only if $C(X)$ is an almost regular ring which does not have any principal maximal ideals if and only if $\operatorname{Rad}\Gamma'_{_2}C(X)= 3$. (English) |
| Keyword:
|
rings of continuous functions |
| Keyword:
|
comaximal graph |
| Keyword:
|
radius |
| Keyword:
|
girth |
| Keyword:
|
dominating number |
| Keyword:
|
clique number |
| Keyword:
|
zero cellularity |
| Keyword:
|
$P$-space |
| Keyword:
|
almost $P$-space |
| Keyword:
|
connected space |
| Keyword:
|
regular ring |
| MSC:
|
54C40 |
| idZBL:
|
Zbl 06674886 |
| idMR:
|
MR3554516 |
| DOI:
|
10.14712/1213-7243.2015.178 |
| . |
| Date available:
|
2016-09-22T15:27:57Z |
| Last updated:
|
2018-10-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145840 |
| . |
| Reference:
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