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 …

The theory of near-rings has arisen in a variety of ways. There is a natural desire to
generalise the theory of rings and skew fields by relaxing some of their defining axioms. It …

Let N be a right near-ring. The class of all near-rings will be denoted by N anc the class of all
O-symmetric near-rings by No. It is well-known that an ideal I* N is ap: ime ideal if and only if …

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 …

(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 …

The following results (9, Exercise 26, p. 10; 1, Theorem 9.2; 8, Theorem III. 1.11) are
known.(A) Let R be a ring with more than one element. Then R is a division ring ifand only if …

1. Introduction. A well known theorem of Cartan-Brauer-Hua states that any division subring
of a division ring D setwise invariant under all inner automorphisms (or more briefly …

It is known that structural matrix rings pro-vide a natural passage from complete matrix rings
to upper and lower triangular matrix rings, and they often explain the peculiarities regarding …

Tame near-rings and N-groups Page 1 Proceedings of the Edinburgh Mathematical Society
(1980), 23, 275-296 © TAME NEAR-RINGS AND N-GROUPS by SD SCOTT (Received 4th …

We treat centralizer near-rings over ring modules in general, with particular emphasis on the
case of free modules. Questions like the following are answered. When is the near-ring a …