| Title:
|
Pure filters and stable topology on BL-algebras (English) |
| Author:
|
Eslami, Esfandiar |
| Author:
|
Haghani, Farhad Kh. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
45 |
| Issue:
|
3 |
| Year:
|
2009 |
| Pages:
|
491-506 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we introduce stable topology and $F$-topology on the set of all prime filters of a BL-algebra $A$ and show that the set of all prime filters of $A$, namely Spec($A$) with the stable topology is a compact space but not $T_0$. Then by means of stable topology, we define and study pure filters of a BL-algebra $A$ and obtain a one to one correspondence between pure filters of $A$ and closed subsets of Max($A$), the set of all maximal filters of $A$, as a subspace of Spec($A$). We also show that for any filter $F$ of BL-algebra $A$ if $\sigma(F)=F$ then $U(F)$ is stable and $F$ is a pure filter of $A$, where $\sigma(F)=\{a\in A|\,y\wedge z=0$ for some $z\in F$ and $y\in a^\perp\}$ and $U(F)=\{P\in $ Spec($A$)\,$\vert\,F\nsubseteq P\}$. (English) |
| Keyword:
|
BL-algebra |
| Keyword:
|
prime filters |
| Keyword:
|
maximal filters |
| Keyword:
|
pure filters |
| Keyword:
|
stable topology |
| Keyword:
|
F-topology |
| MSC:
|
03G25 |
| MSC:
|
06F35 |
| MSC:
|
06F99 |
| MSC:
|
08A72 |
| idZBL:
|
Zbl 1177.03069 |
| idMR:
|
MR2543136 |
| . |
| Date available:
|
2010-06-02T18:45:39Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140014 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
[9] L. Leustean: Representations of Many-Valued Algebras.PhD. Thesis, University of Bucharest 2004. |
| Reference:
|
[10] E. Turunen: Mathematics Behind Fuzzy Logic.Advances in Soft Computing. Physica-Verlag, Heidelberg 1999. Zbl 0940.03029, MR 1716958 |
| Reference:
|
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| . |
