1. Introduction DISTBIBTJTIVB near-rings arise naturally from nilpotent class two groups. Let
(0,+) be such a group and define ab=[a, b]=—a—b+ a-\-b. Then (0,+,•) is a distributive near …

Recently,]~. DE ROBERT has considered the dual concepts of relative projectivity and
relative injectivity that extend the notions of quasi-projective and quasi-injective modules …

Alternative rings are known to satisfy the following two identities.(9 (x, Y, 4= 0,(ii) 0= g (w, x,
y, 4=(wv, y, 4+(w, x,(y, 2))-4x, y, 2)-(2f4 y, x) x, where the associator (a, b, c) is defined by (a …

THEOREM. Let R be an unramified regular local ring, and M a torsion-free R-module of finite
type./f Tor (M, N) 0 for some R-module N offinite type, then Tor M, N) 0 for all j>= i. In this …

The structure of semiprime pri-rings has been obtained by Goldie ([1]). It is the object of this
paper to present an analogous result for a certain class of near-rings. A near-ring is a set JV …

IN the present paper the programme outlined in (3) is oontinued. Its principal aim is the
development of a theory of categories and functors of. R-groups and a more detailed …

NON-ASSOCIATIVE algebraic systems are in some respects simpler than their associative
counterparts. Thus, for example, any groupoid (system closed under a binary, not …

In a previous paper [4](1) we have defined a special Jordan ring to be aa subset of an
associative ring which is a subgroup of the additive group and which is closed under the …

A near-ring is a triple (R,+,· such that (R,+) is a group,(R,·) is a semigroup, and is left
distributive work on near-rings is [1]. A near-ring R is distributively generated if there exists …

Fundamental statements for (associative) rings are that (a) the endomorphisms of each
commutative group (U,+) form a ring and (b) eachring may be embedded in such a ring of …