Properties of Annihilators in Lattice Wajsberg Algebras
A. Ibrahim
P. G. and Research Department of Mathematics, H. H. The Rajah’s College, Pudukkotai-622 001, Tamilnadu, India.
C. Shajitha Begum *
Department of Mathematics, Sri Ramakrishna Engineering College, Coimbatore-641 022, Tamilnadu, India.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Wajsberg algebra, Lattice Wajsberg algebra, WI-ideal, annihilator, homomorphism, isomorphism