On f-Derivations in Residuated Lattices

Mbarek Zaoui\(^a\), Driss Gretete\(^b\), Brahim Fahid\(^{c,*}\)

\(^a\)University of Ibn Tofail National, school of Applied Sciences, Kenitra, Morocco.

\(^b\)University of Ibn Tofail National, school of Applied Sciences, Kenitra, Morocco.

\(^c\)University of Ibn Tofail Superior, School of Technology, Kenitra, Morocco.

Correspondence should be addressed to: zaouimbarek@yahoo.fr, driss.gretete@uit.ac.ma, brahim.fahid@uit.ac.ma

Copyright © 2023 Mbarek Zaoui, Driss Gretete, Brahim Fahid. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: Received: 22 June 2022; Accepted: 15 July 2023; Published Online: 26 September 2023.

Abstract

In this paper, as a generalization of derivation in a residuated lattice, the notion of f-derivation for a residuated lattice is introduced and some related properties of isotone (resp. contractive) f-derivations and ideal f-derivations are investigated. Also, we define principal f-derivation and their properties. Finally, we define the notion of fixed point. In particular, as an application of ideal f-derivation in Heyting algebras, we obtain that the fixed point set is still a residuated lattice.

Keywords:

Residuated Lattice, f-derivation, ideal f-derivation, fixed point set