C. J. Maxson

Centralizer near-rings determined by PID-modules, II

We answer an open problem in radical theory by showing that there exists a zero-symmetric simple near-ringN with identity such thatJ2(N)=N.

Simple near-rings associated with meromorphic products

Let H be a subgroup of G2 and let Mo(G, 2, H) = {f e Mo(G)lf (H) C H}. In this paper we characterize in terms of properties of H when Mo(G, 2, H) is a simple near-ring.

Near-fields associated with invariant linear -relations

In this paper we investigate a construction method for subnearrings of M(G) proposed by H. Wielandt using subgroups of direct powers GIc of G called invariant linear K-relations. If X = 2 we characterize, in terms of properties of these subgroups, when the associated near-rings are near-fields and prove that every near-field arising from an invariant linear 2-relation must be a field.

Forcing Linearity Numbers for Modules over Simple Domains

If R is a simple Noetherian ring and V an R-module, then every homogeneous function on V is an endomorphism, i.e., the forcing linearity number, fln(V), of V is zero, unless R is a domain. Here we consider the problem of finding forcing linearity numbers for modules over simple Noetherian domains. As an application we find the forcing linearity numbers for all finitely generated modules over the first Weyl algebra.

Archimedeisation of Some Ordered Geometric Structures Which are Related to Kinematic Spaces

In view of the aim to “archimedeise ordered kinematic spaces” we compile here the following preliminary work: Connections between order notions like linear order, betweenness, separation and orientation ( = cyclic order) and between ordered, betweenness, separated and oriented groups; archimedeisation of separated groups; complete discussion of the archimedeisation of three types of separated groups derived from unitary associative algebras (A,K) of degree 2 over non archimedean ordered fields (K,+,·,≤).

Meromorphic products determining near-fields

In this paper we continue our investigations of a construction method for subnear-rings of M(G) proposed by H. Wielandt. For a meromorphic product H, H ⊂ G k , G finite, we obtain necessary and sufficient conditions for M(G, k, H) to be a near-field.

Near-Rings of Homogeneous Functions, P 3

This paper is an expanded version of the survey talk (with the same title) presented at the 1995 Conference on near-rings and near-fields held at the Universitat der Bundeswehr Hamburg, 30 July - 5 August, 1995. The paper is divided into three parts, namely the past, the present and predictions (or taking the suggestions of one of the conference participants and a small liberty with spelling), the past, the present, and the phuture. In the next section I will give the general setting, some background information, and discuss some of the earlier results. In the following section I will focus on more recent results and in the final section I will suggest some possible directions for further investigations.

Rings of congruence preserving functions

Let

Some Problems Related to Near-Rings of Mapping

C_0 (G)