Radicals for near-rings (Q2523898)

In his thesis (Tübingen 1963) G. Betsch generalized to (general) near-rings many of the results concerning the radical, quasi-radical and ideal-radical of distributively generated near-rings. In this article the author is able to complete this generalization and even obtains some additional information on the radicals considered by Betsch. For example, the author shows for near-rings satisfying the d.c.c. for right modules that every quasi-regular right module is nilpotent and that the radical is nilpotent if and only if each 0-modular right ideal is a 2-modular right ideal. Furthermore, some other radicals are introduced which have applications to near-rings which do not satisfy the d.c.c. for right modules and makes the study of such near-rings more comprehensible.