Abstract
Let N ≡ <N, +,.> be a (right) near-ring with 1 (we say N is a unitary near-ring)[1] and recall that a near-field is a unitary near-ring in which <N - {0}, . > is a multiplicative group. In [2], Beidelman characterizes near-fields as those unitary near-rings without non-trivial N-subgroups. We show that in the finite case this absence of non-trivial N-subgroups is equivalent to the absence of non-trivial left ideals.
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