On Derivations of Lattice Implication Algebras

Abstract

In this paper, we introduce the notion of derivation in lattice implication algebra, and consider the properties of derivations in lattice implication algebras. We give an equivalent condition to be a derivation of a lattice implication algebra. Also, we characterize the fixed set \(Fix_d(L)\) and \(Kerd\) by derivations. Moreover, we prove that if \(d\) is a derivation of a lattice implication algebra, every filter \(F\) is \(d\)-invariant.