Filter topologies on MV-algebras

Cuicui Luan; Yichuan Yang

doi:10.1007/s00500-017-2574-y

Filter topologies on MV-algebras

Cuicui Luan
, Yichuan Yang^*

^*此作品的通讯作者

数学科学学院

Beihang University

科研成果: 期刊稿件 › 文章 › 同行评审

19 引用（Scopus）

摘要

We show that every MV-algebra A can be naturally equipped with a filter topology such that A is a topological MV-algebra, which improves the main results on C-topological lattice-ordered groups in both Yang (Sci China Ser A 52(11):2397–2403, 2009) and Gusić (Proc Am Math Soc 126(9):2593–2597, 1998). Furthermore, for a 2-divisible MV-algebra A, we show that the filter topological space is Hausdorff if and only if A is semisimple.

源语言	英语
页（从-至）	2531-2535
页数	5
期刊	Soft Computing
卷	21
期	10
DOI	https://doi.org/10.1007/s00500-017-2574-y
出版状态	已出版 - 1 5月 2017

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title = "Filter topologies on MV-algebras",

abstract = "We show that every MV-algebra A can be naturally equipped with a filter topology such that A is a topological MV-algebra, which improves the main results on C-topological lattice-ordered groups in both Yang (Sci China Ser A 52(11):2397–2403, 2009) and Gusi{\'c} (Proc Am Math Soc 126(9):2593–2597, 1998). Furthermore, for a 2-divisible MV-algebra A, we show that the filter topological space is Hausdorff if and only if A is semisimple.",

keywords = "Dense, Filter topology, Hausdorff space, MV-algebra, Semisimple",

author = "Cuicui Luan and Yichuan Yang",

note = "Publisher Copyright: {\textcopyright} 2017, Springer-Verlag Berlin Heidelberg.",

year = "2017",

month = may,

day = "1",

doi = "10.1007/s00500-017-2574-y",

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AU - Luan, Cuicui

AU - Yang, Yichuan

PY - 2017/5/1

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N2 - We show that every MV-algebra A can be naturally equipped with a filter topology such that A is a topological MV-algebra, which improves the main results on C-topological lattice-ordered groups in both Yang (Sci China Ser A 52(11):2397–2403, 2009) and Gusić (Proc Am Math Soc 126(9):2593–2597, 1998). Furthermore, for a 2-divisible MV-algebra A, we show that the filter topological space is Hausdorff if and only if A is semisimple.

AB - We show that every MV-algebra A can be naturally equipped with a filter topology such that A is a topological MV-algebra, which improves the main results on C-topological lattice-ordered groups in both Yang (Sci China Ser A 52(11):2397–2403, 2009) and Gusić (Proc Am Math Soc 126(9):2593–2597, 1998). Furthermore, for a 2-divisible MV-algebra A, we show that the filter topological space is Hausdorff if and only if A is semisimple.

KW - Dense

KW - Filter topology

KW - Hausdorff space

KW - MV-algebra

KW - Semisimple

UR - https://www.scopus.com/pages/publications/85016131919

U2 - 10.1007/s00500-017-2574-y

DO - 10.1007/s00500-017-2574-y

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SN - 1432-7643

VL - 21

SP - 2531

EP - 2535

JO - Soft Computing

JF - Soft Computing

IS - 10

ER -

Filter topologies on MV-algebras

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