### (F,G)-Derivations on a Lattice

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**Authors:**A. AMROUNE, L. ZEDAM AND M. YETTOU

**DOI:**10.46793/KgJMat2205.773A

**Abstract:**

In the present paper, we introduce the notion of (F,G)-derivation on a lattice as a generalization of the notion of (∧,∨)-derivation. This newly notion is based on two arbitrary binary operations F and G instead of the meet (∧) and the join (∨) 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.

**Keywords:**

Lattice, (F,G)-derivation, principal (F,G)-derivation, lattice representation.

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