On near-rings in which the constants form an ideal

Abstract

Let C denote the class of all near-rings which have the property that the subnear-ring of constants forms an ideal. Prominent examples are abstract affine near-rings and a generalisation of these by Feigelstock [1]. In this note we show C forms a variety and construct a proper sub-class such that every N ε C can be embedded into some . It turns out that near-rings have an ideal structure which is similar to the ideal structure of abstract affine near-rings, in contrast to the situation for arbitrary elements of C.