Near-rings and near-fields: proceedings of a conference held at the University of Tubingen, F.R.G., 4-10 August, 1985

Gerhard Betsch (Eds.)0444701915, 9780444701916, 9780080872483

Most topics in near-ring and near-field theory are treated here, along with an extensive introduction to the theory. There are two invited lectures: “Non-Commutative Geometry, Near-Rings and Near-Fields” which indicates the relevance of near-rings and near-fields for geometry, while “Pseudo-Finite Near-Fields” shows the impressive power of model theoretic methods. The remaining papers cover such topics as D.G. near-rings, radical theory, KT-near-fields, matrix near-rings, and applications to systems theory.

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Table of contents :
Content:
Edited by
Page iii

Copyright page
Page iv

Preface
Page v
G. Betsch

List of Registered Participants
Page vi

Introduction
Pages vii-xi

Non-Commutative Geometry, Near-Rings and Near-Fields Original Research Article
Pages 1-13
Johannes André

Pseudo-Finite Near-Fields Original Research Article
Pages 15-29
Ulrich Felgner

On Derivations in Near-Rings Original Research Article
Pages 31-35
Howard E. Bell, Gordon Mason

Embedding of a Near-Ring into a Near-Ring with Identity Original Research Article
Pages 37-40
Gerhard Betsch

The Near-Ring of Some One Dimensional Noncommutative Formal Group Laws Original Research Article
Pages 41-52
James R. Clay

On the Existence of Nil Ideals in Distributive Near-Rings Original Research Article
Pages 53-57
S. De Stefano, S. Di Sieno

Distributive Near-Rings with Minimal Square Original Research Article
Pages 59-62
S. De Stefano, S. Di Sieno

Near-Rings with E-Permutable Translations Original Research Article
Pages 63-72
Celestina Cotti Ferrero

Endomorphism Near-Rings of a Direct Sum of Isomorphic Finite Simple Non-Ablian Groups Original Research Article
Pages 73-78
Y. Fong, J.D.P. Meldrum

On the Ideal Structure in Ultraproducts of Affine Near-Rings Original Research Article
Pages 79-85
Peter Fuchs

Radicals of Ω-Groups Defined by Means of Elements Original Research Article
Pages 87-96
G.K. Gerber

Note on the Completely Prime Radical in Near-Rings Original Research Article
Pages 97-100
N.J. Groenewald

On p-Adic Nearfields Original Research Article
Pages 101-103
Theo Grundhöfer

Euclidean Seminearrings and Nearrings Original Research Article
Pages 105-121
Udo Hebisch, Hanns Joachim Weinert

Ideals and Reachability in Machines Original Research Article
Pages 123-131
Gerhard Hofer

Couplings and Derived Structures Original Research Article
Pages 133-143
Helmut Karzel

Maximal Ideals in Near-Rings Original Research Article
Pages 145-150
Hermann Kautschitsch

D.G. Near-Rings on the Infinite Dihedral Group Original Research Article
Pages 151-166
S.J. Mahmood, J.D.P. Meldrum

Near-Rings Associated with Covered Groups Original Research Article
Pages 167-173
C.J. Maxson

Krull Dimension and Tame Near-Rings Original Research Article
Pages 175-183
J.D.P. Meldrum, A.P.J. Van Der Walt

Solution of an Open Problem Concerning 2-Primitive Near-Rings Original Research Article
Pages 185-191
J H Meyer, Andries P J Van Der Walt

Are the Jacobson-Radicals of Near-Rings M-Radicals? Original Research Article
Pages 193-197
Rainer Mlitz

On Medial Near-Rings Original Research Article
Pages 199-209
Silvia Pellegrini Manara

Near-Rings and Non-Linear Dynamical Systems Original Research Article
Pages 211-232
Günter F. Pilz

Reduced Near-Rings Original Research Article
Pages 233-243
D. Ramakotaiah, V. Sambasivarao

Non-Commutative Spaces and Near-Rings Including PBIBD’s Planar Near-Rings and Non-Commutative Geometry Original Research Article
Pages 245-251
Maic Sasso-Sant

On Geometric Near-Rings Original Research Article
Pages 253-254
Raffaele Scapellato

A Ternary Interpretation of the Infra-Near Rings Original Research Article
Pages 255-266
Mirela Stefänescu

On Two-Sided Ideals in Matrix Near-Rings Original Research Article
Pages 267-271
Andries Pj Van Der Walt

Some Pathology for Radicals in Non-Associative Near-Rings Original Research Article
Pages 273-275
Stefan Veldsman

Partially and Fully Ordered Seminearrings and Nearrings Original Research Article
Pages 277-294
Hanns Joachim Weinert

On Subdirectly Irreducible Near-Rings Which are Fields Original Research Article
Pages 295-298
Richard Wiegandt