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Symmetric bi-derivations of residuated lattices

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Abstract

In this paper, we introduced the notion of symmetric bi-derivations on residuated lattices and investigated some related properties. Some relationships between symmetric bi-derivation and k-isotone, k-contractive and k-ideal symmetric bi-derivations are given. Also, we introduce the sets of k-fixed points of a symmetric bi-derivation and its structure is studied. In particular, we show that the “family” of sets of k-fixed points forms a residuated lattice.

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Author notes

  1. Mbarek Zaoui, Driss Gretete, El Mustapha El Abbassi and Brahim Fahid contributed equally to this work.

Authors and Affiliations

  1. National School of Applied Sciences ENSAK, Ibn Tofail University, BP 241, 14000, Kenitra, Morocco

    Mbarek Zaoui & Driss Gretete

  2. Department of Mathematics, Faculty of Sciences, GrAAF, LMSA, CeReMAR, Mohammed V University of Rabat, Avenue Ibn Batouta, 10000, Rabat, Morocco

    El Mustapha El Abbassi

  3. Superior School of Technology, Ibn Tofail University, BP 241, 14000, Kenitra, Morocco

    Brahim Fahid

Authors
  1. Mbarek Zaoui
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  2. Driss Gretete
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  3. El Mustapha El Abbassi
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  4. Brahim Fahid
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Correspondence to Brahim Fahid.

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Zaoui, M., Gretete, D., El Abbassi, E.M. et al. Symmetric bi-derivations of residuated lattices. Ann Univ Ferrara (2023). https://doi.org/10.1007/s11565-023-00468-3

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  • DOI: https://doi.org/10.1007/s11565-023-00468-3

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