Nearrings, nearfields, and K-loops : proceedings of the Conference on Nearrings and Nearfields, Hamburg, Germany, July 30-August 6, 1995

This present volume is the Proceedings of the 14th International Conference on Near­ rings and Nearfields held in Hamburg at the Universitiit der Bundeswehr Hamburg, from July 30 to August 06, 1995. This Conference was attended by 70 mathematicians and many accompanying persons who represented 22 different countries from all five continents. Thus it was the largest conference devoted entirely to nearrings and nearfields. The first of these conferences took place in 1968 at the Mathematische For­ schungsinstitut Oberwolfach, Germany. This was also the site of the conferences in 1972, 1976, 1980 and 1989. The other eight conferences held before the Hamburg Conference took place in eight different countries. For details about this and, more­ over, for a general historical overview of the development of the subject, we refer to the article "On the beginnings and development of near-ring theory" by G. Betsch [3]. During the last forty years the theory of nearrings and related algebraic struc­ tures like nearfields, nearmodules, nearalgebras and seminearrings has developed into an extensive branch of algebra with its own features. In its position between group theory and ring theory, this relatively young branch of algebra has not only a close relationship to these two more well-known areas of algebra, but it also has, just as these two theories, very intensive connections to many further branches of mathematics. Front Matter....Pages i-xiii From Nearrings and Nearfields to K-Loops....Pages 1-20 On Non-Zerosymmetric Near-Rings with Minimum Condition....Pages 21-33 Near-Rings of Homogeneous Functions, P 3 ....Pages 35-46 The Structure of Ω-Groups....Pages 47-137 Ordered Nearfields....Pages 139-149 Strongly Idempotent Seminearrings and Their Prime Ideal Spaces....Pages 151-166 A Note on Simple Composition Rings....Pages 167-173 The Cardinalities of the Endomorphism Near-Rings I(G), A(G ), AND E(G) for All Groups G with | G| ≤ 31....Pages 175-178 Polynomial Near-Rings: Polynomials with Coefficients from a Near-Ring....Pages 179-190 On Derivations in Near-Rings, II....Pages 191-197 Near-Rings and Rings Generated by Homomorphisms on Groups....Pages 199-210 Special Radicals of Ω-Groups....Pages 211-218 Quasi-Ideals and Bi-Ideals in Categories....Pages 219-224 Seminearrings of Polynomials Over Semifields: A Note on Blackett’s Fredericton Paper....Pages 225-236 Circles and Their Interior Points from Field Generated Ferrero Pairs....Pages 237-246 On Direct Decompositions in Group Near-Rings....Pages 247-252 On Involution Sets Induced by Neardomains....Pages 253-258 Superprime Near-Rings....Pages 259-267 Involutions on Universal Algebras....Pages 269-282 Fibered Incidence Loops by Neardomains....Pages 283-286 The Structure Group of Certain K-Loops....Pages 287-294 Some Examples of Indecomposable Modules....Pages 295-299 Central Bol Loops....Pages 301-310 Products on Products on Groups....Pages 311-323 Topological N -Groups Where the Nearrings are Real Nearrings....Pages 325-333 Tensor Product of Near-Ring Modules....Pages 335-342 Nilpotence and Endomorphism Near-Rings....Pages 343-352 Distributively Generated Subrings of Homogeneous Maps....Pages 353-356 Composition Near-Rings....Pages 357-372 Categories of Near-Rings....Pages 373-375 The Inner Automorphism Nearrings I( G ) on all Nonabelian Groups G of Order | G | ≤ 100....Pages 377-402 Special Quasigroups and Steiner Systems....Pages 403-416 On the Non-Simplicity of a Subring of M(G) ....Pages 417-429 Near-Rings in Connection with Non-Abelian Cohomology of Groups....Pages 431-435 On the Salient Properties of Near-Ring Radicals....Pages 437-444 Back Matter....Pages 445-449 This present volume is the Proceedings of the 14th International Conference on NearƯ rings and Nearfields held in Hamburg at the Universitiit der Bundeswehr Hamburg, from July 30 to August 06, 1995. This Conference was attended by 70 mathematicians and many accompanying persons who represented 22 different countries from all five continents. Thus it was the largest conference devoted entirely to nearrings and nearfields. The first of these conferences took place in 1968 at the Mathematische ForƯ schungsinstitut Oberwolfach, Germany. This was also the site of the conferences in 1972, 1976, 1980 and 1989. The other eight conferences held before the Hamburg Conference took place in eight different countries. For details about this and, moreƯ over, for a general historical overview of the development of the subject, we refer to the article "On the beginnings and development of near-ring theory" by G. Betsch [3]. During the last forty years the theory of nearrings and related algebraic strucƯ tures like nearfields, nearmodules, nearalgebras and seminearrings has developed into an extensive branch of algebra with its own features. In its position between group theory and ring theory, this relatively young branch of algebra has not only a close relationship to these two more well-known areas of algebra, but it also has, just as these two theories, very intensive connections to many further branches of mathematics This present volume is the Proceedings of the 14th International Conference on Nearrings and Nearfields held in Hamburg at the Universität der Bundeswehr Hamburg, from July 30 to August 6, 1995. It contains the written version of five invited lectures concerning the development from nearfields to K-loops, non-zerosymmetric nearrings, nearrings of homogeneous functions, the structure of Omega-groups, and ordered nearfields. They are followed by 30 contributed papers reflecting the diversity of the subject of nearrings and related structures with respect to group theory, combinatorics, geometry, topology as well as the purely algebraic structure theory of these algebraic structures. Audience: This book will be of value to graduate students of mathematics and algebraists interested in the theory of nearrings and related algebraic structures. Proceedings of the Conference on Nearrings and Nearfield, Hamburg, Germany, July 30-August 6, 1995