Properties of Annihilators in Lattice Wajsberg Algebras

In this paper, we introduce the notion of the annihilator in lattice Wajsberg algebra and investigate some related properties of it. We show that the annihilator is a WI-ideal. In further note, we discuss relationship between the annihilator and a WI-ideal in the article. Moreover, we investigate some properties of the lattice implication homomorphism image of annihilators, and also give the necessary and sufficient condition of the lattice implication homomorphism image, and we obtain lattice implication homomorphism and isomorphism inverse images of annihilators in lattice from Wajsberg algebras.