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\((\odot ,\vee )\)-Derivations on MV-algebras

  • Foundation, algebraic, and analytical methods in soft computing
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Abstract

Let A be an MV-algebra. An \((\odot ,\vee )\)-derivation on A is a map \(d: A\rightarrow A\) satisfying: \(d(x \odot y) = (d(x) \odot y) \vee (x \odot d(y))\) for  all \(x, y \in A\). This paper initiates the study of \((\odot ,\vee )\)-derivations on MV-algebras. Several families of \((\odot ,\vee )\)-derivations on an MV-algebra are explicitly constructed to give realizations of the underlying lattice of an MV-algebra as lattices of \((\odot ,\vee )\)-derivations. Furthermore, \((\odot ,\vee )\)-derivations on a finite MV-chain are enumerated and the underlying lattice is described.

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Funding

The work is partially supported by CNNSF (Grants: 12171022, 62250001).

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Authors and Affiliations

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

    Xueting Zhao & Yichuan Yang

  2. School of Mathematics and Statistics, Jiangxi Normal University, Nanchang, 330022, China

    Aiping Gan

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  1. Xueting Zhao
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  2. Aiping Gan
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Zhao, X., Gan, A. & Yang, Y. \((\odot ,\vee )\)-Derivations on MV-algebras. Soft Comput 28, 1833–1849 (2024). https://doi.org/10.1007/s00500-023-09384-2

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