Near-rings and near-ring modules

Abstract

Dickson [11], in 1905,first gave examples of finite nearfields, which, in 1907, were used by 0. Veblen and J.H. MaclaganWedderburn [26] to construct finite non-desarguesian and non-pascalian geometries. The problem of characterising all finite near-fields remained open until Zassenhaus [28], in 1936, showed the addition of seven proper finite near-fields to the list of Dickson's, gave the complete picture. It appears that near-rings proper were first looked at in 1932 by H. Fitting [12]. Not long after, O. Taussky [25] and B.H. Neumann [22] considered rings in which addition need not be commutative. The first real structural theorems on nearrings are due to D.W. Blackett [8], who in 1953 extended the theory of simple and semi-simple rings to near-rings. These extensions, which exhibit a great deal of ingenuity, mark, in the author's opinion, the beginning of the first serious attempt to understand near-rings. Show more