Pure filters and stable topology on BL-algebras

Eslami, Esfandiar, and Haghani, Farhad Kh.. "Pure filters and stable topology on BL-algebras." Kybernetika 45.3 (2009): 491-506. <http://eudml.org/doc/37672>.

@article{Eslami2009,
abstract = {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 $\sigma (F)=\lbrace a\in A|\,y\wedge z=0$ for some $z\in F$ and $y\in a^\perp \rbrace $ and $U(F)=\lbrace P\in $ Spec($A$) $\vert \,F\nsubseteq P\rbrace $.},
author = {Eslami, Esfandiar, Haghani, Farhad Kh.},
journal = {Kybernetika},
keywords = {BL-algebra; prime filters; maximal filters; pure filters; stable topology; F-topology; BL-algebra; prime filters; maximal filters; pure filters; stable topology; -topology},
language = {eng},
number = {3},
pages = {491-506},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Pure filters and stable topology on BL-algebras},
url = {http://eudml.org/doc/37672},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Eslami, Esfandiar
AU - Haghani, Farhad Kh.
TI - Pure filters and stable topology on BL-algebras
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 3
SP - 491
EP - 506
AB - 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 $\sigma (F)=\lbrace a\in A|\,y\wedge z=0$ for some $z\in F$ and $y\in a^\perp \rbrace $ and $U(F)=\lbrace P\in $ Spec($A$) $\vert \,F\nsubseteq P\rbrace $.
LA - eng
KW - BL-algebra; prime filters; maximal filters; pure filters; stable topology; F-topology; BL-algebra; prime filters; maximal filters; pure filters; stable topology; -topology
UR - http://eudml.org/doc/37672
ER -