On \(f\)-Derivations of Lattice Implication Algebras

Abstract

In this paper, we introduce the notion of \(f\)-derivations and investigate the properties of \(f\)-derivations of lattice implication
algebras. We provide an equivalent condition for an isotone \(f\)-derivation in a lattice implication algebra. Additionally, we
characterize the fixed set \({Fix_d}(L)\) and \(\mathrm{Kerd}\) by \(f\)-derivations. Furthermore, we introduce
normal filters and obtain some properties of normal filters in lattice implication algebras.