Different nil radicals for near-rings

Abstract

It is well known that there are a number of different nonequivalent definitions of a prime near-ring. In this paper we show that this give rise to a number of different upper nil radicals which all coincide with the usual upper nil radical in the case of associative rings.

Keywords:Prime near-ring; Hoehnke radical; nil radical

Quaestiones Mathematicae 30(2007), 207–217