Articles

On generalized (α, β)-derivations on lattices

Published in: Quaestiones Mathematicae
Volume 34 , issue 4 , 2011 , pages: 417–424

DOI: 10.2989/16073606.2011.640439

Author(s): Muhammad , Anwar Chaudhry* Center for Advanced Studies in Pure and Applied Mathematics, Pakistan , Zafar Ullah Center for Advanced Studies in Pure and Applied Mathematics, Pakistan

Keywords: 03G16 , 06C05 , 17A36 , 03G16 , 06C05 , 17A36

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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, ”

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