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

The study of near-rings is motivated by consideration of the system generated by the
endomorphisms of a (not necessarily commutative) group. Such endomorphism near-rings …

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. 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 …

In ring theory there is the following theorem (cf.[1], p. 39): If R is a ring satisfying the
descending chain condition for left ideals, then the following three conditions are …

Part of the recent work on near-rings has been concerned with sufficient conditions for near-
rings to be rings. Ligh [7], by proving that distributively-generated Boolean near-rings are …

The theory of simple and semi-simple dg near-rings has been discussed in some detail
(cf.[1, 2, 3]). In this article we make a start on the radical theory for distributively generated …

A near-ring is a triple (G,+,*) such that (G,+) is a group,(G,*) is a semigroup, and* is left
distributive over+; ie for a, b, ce G, a*(b+ c)= a* b+ a* c. For examples of near-rings that arise …

In the theory of near-rings the near-rings with identities occupy a role analogous to that in
ring theory of rings with identities. Specifically, every near-ring may be embedded in a near …

(gnl) n2= g (n1n2) for every selection of ni and n2 from N and g from G. If" operating by n" is
defined as right multiplication by n, a near-ring N is itself a right N-group. The additive …