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 …

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. 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 …

Publisher Summary This chapter presents an account of this correspondence, which turns
out to be more complex than in the ring case. Let (R,+,·) be a right near-ring with identity 1. R …

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 …

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 …

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 …

The set F [[x]] of power series over a field F under the usual operations of addition and
multiplication is a local ring in the sense that the set L of nonunits in F [[x]] is an ideal. If we …

In 1937, Wielandt determined the structure of (right) near-rings with identity, which have only
the trivial ideals I and satisfy the descending chain condition on right ideals [11]. Since 1951 …

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 …