0. Introduction. In the following lecture I will first define a certain class of not necessarily
additive maps from an abelian semigroup A into an abelian group B, which factor uniquely …

One of the ways in which matrix near-rings as defined by Meldrum and van der Walt differ
from matrix rings is that the correspondence between ideals in the matrix near-ring and …

Since the discovery of the existence of the injective hull of an arbitrary module
independently in 1952 by Shoda and in 1953 by Eckmann and Schopf, there have been …

In analogy to the elementwise definition of von Neumann regular rings an $ R $-module $ M
$ is called regular if given any element $ m\in M $ there exists $ f\in {\operatorname {Hom} …

1. Introduction. An element a of a ring 9Î is said to be regular if there exists an element x of dt
such that axa= a. A ring 9î with unit element, every element of which is regular, is a regular …

1. Introduction. Group near-rings have been defined by Meldrum [2, 3] and extended slightly
in Mahmood and Meldrum [1]. In all these cases only dg near-rings were considered and the …

In 1987, APJ van der Walt [1] overcame the difficulties caused by the lack of one distributive
law in near-rings in order to create matrix near-rings with the property that when the near …

Matrix near-rings over general near-rings were introduced in [S]; more material appeared in
[69]. Most of these results are concerned with the transfer of properties from the near-ring R …

1. Introduction. As in the theory of groups, many of the more intricate questions of ring
structure appear as extension problems. The structure of nilpotent algebras, anid that of …

Special radical classes of near-rings are defined and investigated. It is shown that our
approach, which differs from previous ones, does cater for all the well-known radicals of …