In recent years there has arisen an interest in algebraic systems with binary compositions of
addition and multiplication satisfying all the ring aXiOm S, save possibly, one of the …

1. Introduction. Near-ringers seem to have reluctantly concluded that in most cases it does
not make sense to speak about a near-ring of matrices over an arbitrary near-ring, cf …

The connection between the structure of a near-ring and that of the group on which it acts is
used to obtain results concerning the structure of near-rings. A generalized R series is …

In the second section we show that if J (M) is the radical of a module M over a near-ring R,
then J (M/J (M))= 0. Also, if A is a submodule of M and J (M/A)= 0, then J (M) g A. These …

1. Introduction. The ring structure of the endomorphisms of a commutative group is well
known. Most of the ring properties do not hold for the endomorphisms of a noncommutative …

Algebraic systems with addition and multiplication which satisfy all of the skew-field axioms
except possibly one of the distributive laws have been studied occasionally. Dickson [l] gave …

DISTRIBUTIVELY GENERATED NEAR-RINGS Page 1 DISTRIBUTIVELY GENERATED
NEAR-RINGS (I. IDEAL THEORY) By A. FROHLICH [Received 9 March 1957.—Read 14 March …

1. Introduction. In a recent paper [1], DW Blackett extended a number of results from the
theory of semisimple rings to semisimple near-rings. Whereas a semisimple ring is ordinarily …

PRIMITIVITY IN MATRIX NEAR-RINGS Page 1 Quaestiones Mathematicae - 9 (1986). 459-469
PRIMITIVITY IN MATRIX NEAR-RINGS Andries PJ van der Walt ABSTRACT. The relationships …

1* Introduction* We shall limit ourselves to near-rings for which addition is commutative.
They will be known as abelian nearrings. We assume that the distributive law (δ+ c) a—ba+ …