Soft Computing

, Volume 21, Issue 10, pp 2531–2535 | Cite as

Filter topologies on MV-algebras

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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 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.

Keywords

MV-algebra Filter topology Hausdorff space Semisimple Dense 

References

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  6. Yang Y (2009) The C-topology on lattice-ordered groups. Sci China Ser A 52(11):2397–2403MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Mathematics and System SciencesBeihang UniversityBeijingChina

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