A Generalization of a Theorem of Zassenhaus
Canadian mathematical bulletin, Tome 12 (1969) no. 5, pp. 677-678
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A near-ring is a triple (R, +,.) such that (R, +) is a group, (R,.) is a semigroup and. is left distributive over +; i.e. w(x + z) = wx + wz for each w, x, z in R. A near-field is a nearring such that the nonzero elements form a group under multiplication. Zassenhaus [3] showed that if R is a finite near-field, then (R, + ) is abelian. B.H. Neumann [1] extended this result to all near-fields. Recently another proof of this important result was given by Zemmer [4]. The purpose of this note is to give another generalization of the Zassenhaus theorem. In fact, we shall prove the following.
Ligh, Steve. A Generalization of a Theorem of Zassenhaus. Canadian mathematical bulletin, Tome 12 (1969) no. 5, pp. 677-678. doi: 10.4153/CMB-1969-089-2
@article{10_4153_CMB_1969_089_2,
author = {Ligh, Steve},
title = {A {Generalization} of a {Theorem} of {Zassenhaus}},
journal = {Canadian mathematical bulletin},
pages = {677--678},
year = {1969},
volume = {12},
number = {5},
doi = {10.4153/CMB-1969-089-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-089-2/}
}
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