The Characterization of a Lattice Homomorphism

Abstract

We shall give a simple characterization of a lattice homomorphism from a linear lattice E to a linear lattice F. This paper is motivated by the following two theorems in Kaplan [2] :If ϕ is a lattice homomorphism, then ϕt(Fb) is an ideal in Eb.(2) If ϕ is a lattice homomorphism, then ϕtt is a lattice homomorphism from ϕbb into ϕbb.The main theorem is stated and proved in section 3. In section 1, we shall give notations and in section 2, we shall prove a main lemma. For details, we refer to Vulikh [3].