Articles
On generalized (α, β)-derivations on lattices
DOI:
10.2989/16073606.2011.640439
Author(s):
Muhammad, Anwar Chaudhry*Center for Advanced Studies in Pure and Applied Mathematics, Pakistan, Zafar UllahCenter for Advanced Studies in Pure and Applied Mathematics, Pakistan,
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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