On generalized (α, β)-derivations on lattices

Abstract

In this paper we introduce the notion of a generalized (α, β, d)-derivation on a lattice, with associated two sided α-derivation d, and investigate some related results. Among some other results we prove that “Let be a modular lattice and G a generalized (α, β, d)-derivation, with associated two sided α-derivation d, on L. If a is an increasing endomorphism on L satisfying α(x) ≤ β(x) for x ∈ L, then the following conditions are equivalent: (a) G is isotone generalized (α, β, d)-derivation on L, ”