Abstract
is one-to-one of F upon F. (See [2],' Appendix.) R. H. Bruck has shown that fields F having additive endomorphisms 0 satisfying (1.2), and yet not right multiplications, actually exist. The author, in [I], has therefore called a not alternative, right alternative division ring B (necessarily of characteristic two) a Bruck ring if it is two dimensional over some field F and if multiplication in B is given by (1.1). The field F turns out to be the left nucleus of B and, in all the examples given by Bruck, is a simple transcendental extension of a field of characteristic two, and thus imperfect. In this note we give an elementary proof that this situation must of necessity occur:
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