Geodesic
$(F,G)$-Derivations on a Lattice
Kragujevac Journal of Mathematics, Tome 46 (2022) no. 5, p. 773 .

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In the present paper, we introduce the notion of $(F,G)$-derivation on a lattice as a generalization of the notion of $(\wedge,\vee)$-derivation. This newly notion is based on two arbitrary binary operations $F$ and $G$ instead of the meet $(\wedge)$ and the join $(\vee)$ operations. Also, we investigate properties of $(F,G)$-derivation on a lattice in details. Furthermore, we define and study the notion of principal $(F,G)$-derivations as a particular class of $(F,G)$-derivations. As applications, we provide two representations of a given lattice in terms of its principal $(F,G)$-derivations.
Classification : 06B05, 03G10 06B99
Keywords: Lattice, $(F;G)$-derivation, principal $(F;G)$-derivation, lattice representation 
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     author = {Abdelaziz Amroune and Lemnaouar Zedam and Mourad Yettou},
     title = {$(F,G)${-Derivations} on a {Lattice}},
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Abdelaziz Amroune; Lemnaouar Zedam; Mourad Yettou. $(F,G)$-Derivations on a Lattice. Kragujevac Journal of Mathematics, Tome 46 (2022) no. 5, p. 773 . http://geodesic.mathdoc.fr/item/KJM_2022_46_5_a8/