The distributive elements of a near-field
Abstract
In this thesis, we investigated some properties of (left)near fields and derived some results. We are focusing on D(α, β) which is the generalized set of distributive elements of a nearfield. In particular, we investigated some conditions on α,β, α+β for D(α, β) to be a subfield of Fqn. In nearfield theory the two distributive laws can not hold at the same time. So in term of left nearfield and near-ring, the right distributivity does not hold and to solve the problem, we defined a set of all distributive elements called D(R).
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