Geodesic
f-Fixed Points of Isotone f-Derivations on a Lattice
Discussiones Mathematicae. General Algebra and Applications, Tome 39 (2019) no. 1, pp. 69-89.

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In a recent paper, Çeven and Öztürk have generalized the notion of derivation on a lattice to f-derivation, where f is a given function of that lattice into itself. Under some conditions, they have characterized the distributive and modular lattices in terms of their isotone f-derivations. In this paper, we investigate the most important properties of isotone f-derivations on a lattice, paying particular attention to the lattice (resp. ideal) structures of isotone f-derivations and the sets of their f-fixed points. As applications, we provide characterizations of distributive lattices and principal ideals of a lattice in terms of principal f-derivations.
Keywords: lattice, isotone f-derivation, principal f-derivation, f-fixed points set 
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Zedam, Lemnaouar; Yettou, Mourad; Amroune, Abdelaziz. f-Fixed Points of Isotone f-Derivations on a Lattice. Discussiones Mathematicae. General Algebra and Applications, Tome 39 (2019) no. 1, pp. 69-89. http://geodesic.mathdoc.fr/item/DMGAA_2019_39_1_a5/

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