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Pure filters and stable topology on BL-algebras
Kybernetika, Tome 45 (2009) no. 3, pp. 491-506 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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($A$)\,$\vert\,F\nsubseteq P\}$.
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($A$)\,$\vert\,F\nsubseteq P\}$.
Classification : 03G25, 06F35, 06F99, 08A72
Keywords: BL-algebra; prime filters; maximal filters; pure filters; stable topology; F-topology 
@article{KYB_2009_45_3_a8,
     author = {Eslami, Esfandiar and Haghani, Farhad Kh.},
     title = {Pure filters and stable topology on {BL-algebras}},
     journal = {Kybernetika},
     pages = {491--506},
     year = {2009},
     volume = {45},
     number = {3},
     mrnumber = {2543136},
     zbl = {1177.03069},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2009_45_3_a8/}
}
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Eslami, Esfandiar; Haghani, Farhad Kh. Pure filters and stable topology on BL-algebras. Kybernetika, Tome 45 (2009) no. 3, pp. 491-506. http://geodesic.mathdoc.fr/item/KYB_2009_45_3_a8/

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