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Orthomodular lattices as L-algebras

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Abstract

We first prove that the axioms system of orthomodular L-algebra (O-L-algebras for short) as given in [Rump: Forum Mathematicum, 30(4), 2018: 973–995] are not independent by giving an independent axiom one. Then, two conditions for KL-algebras to be Boolean are provided. Furthermore, some theorems of Holland are reproved using the self-similar closure of OM-L-algebras. In particular, the monoid operation of the self-similar closure is shown to be commutative.

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Acknowledgements

Y. Yang: supported by CNNSF (Grant:11771004). Y. Wu: Supported by Hebei Youth Natural Science Fund (Grant: A2019403031).

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Authors and Affiliations

  1. School of Mathematical Sciences, Beihang University, Shahe Campus, Beijing, 102206, China

    Yali Wu & Yichuan Yang

  2. School of Mathematics and Physics, Hebei GEO University, Shijiazhuang, 050031, China

    Yali Wu

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  1. Yali Wu
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  2. Yichuan Yang
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Correspondence to Yichuan Yang.

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Communicated by A. Di Nola.

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Wu, Y., Yang, Y. Orthomodular lattices as L-algebras. Soft Comput 24, 14391–14400 (2020). https://doi.org/10.1007/s00500-020-05242-7

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  • DOI: https://doi.org/10.1007/s00500-020-05242-7

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