Inverse topology in MV-algebras
Fereshteh Forouzesh; Farhad Sajadian; Mahta Bedrood
Mathematica Bohemica (2019)
- Volume: 144, Issue: 3, page 273-285
- ISSN: 0862-7959
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topForouzesh, Fereshteh, Sajadian, Farhad, and Bedrood, Mahta. "Inverse topology in MV-algebras." Mathematica Bohemica 144.3 (2019): 273-285. <http://eudml.org/doc/294509>.
@article{Forouzesh2019,
abstract = {We introduce the inverse topology on the set of all minimal prime ideals of an MV-algebra $A$ and show that the set of all minimal prime ideals of $A$, namely $\{\rm Min\}(A)$, with the inverse topology is a compact space, Hausdorff, $T_\{0\}$-space and $T_\{1\}$-space. Furthermore, we prove that the spectral topology on $\{\rm Min\}(A)$ is a zero-dimensional Hausdorff topology and show that the spectral topology on $\{\rm Min\}(A)$ is finer than the inverse topology on $\{\rm Min\}(A)$. Finally, by open sets of the inverse topology, we define and study a congruence relation of an MV-algebra.},
author = {Forouzesh, Fereshteh, Sajadian, Farhad, Bedrood, Mahta},
journal = {Mathematica Bohemica},
keywords = {minimal prime; spectral topology; inverse topology; congruence},
language = {eng},
number = {3},
pages = {273-285},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Inverse topology in MV-algebras},
url = {http://eudml.org/doc/294509},
volume = {144},
year = {2019},
}
TY - JOUR
AU - Forouzesh, Fereshteh
AU - Sajadian, Farhad
AU - Bedrood, Mahta
TI - Inverse topology in MV-algebras
JO - Mathematica Bohemica
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 144
IS - 3
SP - 273
EP - 285
AB - We introduce the inverse topology on the set of all minimal prime ideals of an MV-algebra $A$ and show that the set of all minimal prime ideals of $A$, namely ${\rm Min}(A)$, with the inverse topology is a compact space, Hausdorff, $T_{0}$-space and $T_{1}$-space. Furthermore, we prove that the spectral topology on ${\rm Min}(A)$ is a zero-dimensional Hausdorff topology and show that the spectral topology on ${\rm Min}(A)$ is finer than the inverse topology on ${\rm Min}(A)$. Finally, by open sets of the inverse topology, we define and study a congruence relation of an MV-algebra.
LA - eng
KW - minimal prime; spectral topology; inverse topology; congruence
UR - http://eudml.org/doc/294509
ER -
References
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