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 …

Throughout this article we shall assume that R is a distributively generated (dg) near-ring
with an identity element and satisfies the descending chain condition (dcc) on left …

1. Introduction. Since the appearance in 1949 of the fundamental paper [3] by McCoy on
prime ideals in general rings, quite a number of ideal theoretic results which are well known …

1. Introduction. The equiprime, strongly equiprime and uniformly strongly equiprime radicals
were recently introduced by the present authors, together with S. Veldsman. We show that …

1. Introduction. The radical N of a ring R, in which the right (left) ideals satisfy the descending
chain condition, is usually defined as the join of all nil right (left) ideals in R. It is well known …

The second section is concerned with what will be called'formation radicals', and we show
that for any such radical 3? there exists a unique'complementary'radical££'which is again a …

In an attempt to extend to near-rings the concept of Jacobson radical (for rings), BETSCI~[1]
has investigated the ideals Jr (N), v= 0, 1, 2 and the fight ideal D (N) for a near-ring N.(For a …

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. PRELIMINARY DEFINITIONS We will denote a near-ring by N and the class of all near-
rings by N, where it is understood that near-rings have the right: distributive property, ie (a+ …

Quasi-ideals in near-rings Page 1 九州大学学術情報リポジトリ Kyushu University Institutional
Repository Quasi-ideals in near-rings Yakabe, Iwao Department of Mathematics, College of …