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A New Characterization of Finite Prime Fields

Published online by Cambridge University Press:  20 November 2018

Carlton J. Maxson
Carlton J. Maxson*
Affiliation:
State University College, Fredonia, New York
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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 3 , August 1968 , pp. 381 - 382
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Beidleman, J. C., A radical for near-ring modules. Mich. Math. J. 12 (1965) 377-383.Google Scholar
2. Beidleman, J. C., On near-rings and near-ring modules. (Doctoral dissertation, The Pennsylvania State University, 1964.)Google Scholar
3. Clay, J.R. and Malone, J. J. Jr The near-rings with identities on certain finite groups. Math. Scand. 19 (1966) 146-150.Google Scholar