| Title:
|
On graph associated to co-ideals of commutative semirings (English) |
| Author:
|
Talebi, Yahya |
| Author:
|
Darzi, Atefeh |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
58 |
| Issue:
|
3 |
| Year:
|
2017 |
| Pages:
|
293-305 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be a commutative semiring with non-zero identity. In this paper, we introduce and study the graph $\Omega(R)$ whose vertices are all elements of $R$ and two distinct vertices $x$ and $y$ are adjacent if and only if the product of the co-ideals generated by $x$ and $y$ is $R$. Also, we study the interplay between the graph-theoretic properties of this graph and some algebraic properties of semirings. Finally, we present some relationships between the zero-divisor graph $\Gamma(R)$ and $\Omega(R)$. (English) |
| Keyword:
|
semiring |
| Keyword:
|
co-ideal |
| Keyword:
|
maximal co-ideal |
| MSC:
|
05C75 |
| MSC:
|
16Y60 |
| idZBL:
|
Zbl 06837066 |
| idMR:
|
MR3708774 |
| DOI:
|
10.14712/1213-7243.2015.219 |
| . |
| Date available:
|
2017-11-22T09:19:19Z |
| Last updated:
|
2019-10-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146913 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| . |
