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TitleNearrings, Nearfields and K-Loops [electronic resource] : Proceedings of the Conference on Nearrings and Nearfields, Hamburg, Germany, July 30-August 6,1995 / edited by Gerhard Saad, Momme Johs Thomsen
ImprintDordrecht : Springer Netherlands, 1997
Connect tohttp://dx.doi.org/10.1007/978-94-009-1481-0
Descript XIV, 450 p. online resource

SUMMARY

This present volume is the Proceedings of the 14th International Conference on Nearยญ 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 Forยญ 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, moreยญ 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 strucยญ 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


CONTENT

Invited Addresses -- From nearrings and nearfields to K-Loops -- On non-zerosymmetric near-rings with minimum condition -- Near-rings of homogeneous functions, P3 -- The structure of ?-groups -- Ordered nearfields -- Contributed Papers -- Strongly idempotent seminearrings and their prime ideal spaces -- A note on simple composition rings -- The cardinalities of the endomorphism near-rings I(G), A(G), and E(G) for all groups G with | ? 31 -- Polynomial near-rings: Polynomials with coefficients from a near-ring -- On derivations in near-rings, II -- Near-rings and rings generated by homomorphisms on groups -- Special radicals of ?-groups -- Quasi-ideals and bi-ideals in categories -- Seminearrings of polynomials over semifields: A note on Blackettโ{128}{153}s Fredericton paper -- Circles and their interior points from field generated Ferrero pairs -- On direct decompositions in group near-rings -- On involution sets induced by neardomains -- Superprime near-rings -- Involutions on universal algebras -- Fibered incidence loops by neardomains -- The structure group of certain K-Loops -- Some examples of indecomposable modules -- Central Bol loops -- Products on products on groups -- Topological N-groups where the nearrings are real nearrings -- Tensor product of near-ring modules -- Nilpotence and endomorphism near-rings -- Distributively generated subrings of homogeneous maps -- Composition near-rings -- Categories of near-rings -- The inner automorphism nearrings I(G) on all Nonabelian Groups G of Order | ? 100 -- Special quasigroups and Steiner systems -- On the non-simplicity of a subring of M(G) -- Near-rings in connection with non-abelian cohomology of groups -- On the salient properties of near-ring radicals


Mathematics Algebra Group theory Nonassociative rings Rings (Algebra) Geometry Mathematical logic Combinatorics Mathematics Algebra Mathematical Logic and Foundations Non-associative Rings and Algebras Group Theory and Generalizations Combinatorics Geometry



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