Geodesic
A New Characterization of Finite Prime Fields
Canadian mathematical bulletin, Tome 11 (1968) no. 3, pp. 381-382

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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. 
Maxson, Carlton J. A New Characterization of Finite Prime Fields. Canadian mathematical bulletin, Tome 11 (1968) no. 3, pp. 381-382. doi: 10.4153/CMB-1968-043-8
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     author = {Maxson, Carlton J.},
     title = {A {New} {Characterization} of {Finite} {Prime} {Fields}},
     journal = {Canadian mathematical bulletin},
     pages = {381--382},
     year = {1968},
     volume = {11},
     number = {3},
     doi = {10.4153/CMB-1968-043-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-043-8/}
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