Near-Rings and Near-Fields book cover

Near-Rings and Near-Fields

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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Published: April 1987

Imprint: North-holland

ISBN: 978-0-444-70191-6

Contents

  • Invited Lectures: Non-Commutative Geometry, Near-Rings and Near-Fields (J. André). Pseudo-Finite Near-Fields (U. Felgner). Communications: On Derivations in Near-Rings (H.E. Bell and G. Mason). Embedding of a Near-Ring into a Near-Ring with Identity (G. Betsch). The Near-Ring of Some One-Dimensional Noncommutative Formal Group Laws (J.R. Clay). On the Existence of Nil Ideals in Distributive Near-Rings (S. De Stefano and S. Di Sieno). Distributive Near-Rings with Minimal Square (S. De Stefano and S. Di Sieno). Near-Rings with E-Permutable Translations (C. Cotti Ferrero). Endomorphism Near-Rings of a Direct Sum of Isomorphic Finite Simple Non-Abelian Groups (Y. Fong and J.D.P. Meldrum). On the Ideal Structure in Ultraproducts of Affine Near-Rings (P. Fuchs). Radicals of &OHgr;-Groups by Means of Elements (G.K. Gerber). Note on the Completely Prime Radical in Near-Rings (N.J. Groenewald). On p-adic Near-Fields (Th. Grundhöfer). Euclidean Seminear-Rings and Near-Rings (U. Hebisch and H.J. Weinert). Ideals and Reachability in Machines (G. Hofer). Couplings and Derived Structures (H. Karzel). Maximal Ideals in Near-Rings (H. Kautschitsch). D.G. Near-Rings on the Infinite Dihedral Group (S.J. Mahmood and J.D.P. Meldrum). Near-Rings Associated with Covered Groups (C.J. Maxson). Krull Dimension and Tame Near-Rings (J.D.P. Meldrum and A.P.J. van der Walt). Solution of an Open Problem Concerning 2-Primitive Near-Rings (J.H. Meyer and A.P.J. van der Walt). Are the Jacobson-Radicals of Near-Rings M-Radicals? (R. Mlitz). On Medial Near-Rings (S. Pellegrini Manara). Near-Rings and Non-Linear Dynamical Systems (G. Pilz). Reduced Near-Rings (D. Ramakotaiah and V. Sambasivarao). Non-Commutative Spaces and Near-Rings including PBIBD's Planar Near-Rings and Non-Commutative Geometry (M. Sasso-Sant). On Geometric Near-Rings (R. Scapellato). A Ternary Interpretation of the Infra-Near Rings (M. Stefanescu). On Two-Sided Ideals in Matrix Near-Rings (A.P.J. van der Walt). Some Pathology for Radicals in Non-Associative Near-Rings (S. Veldsman). Partially and Fully Ordered Seminear-Rings and Near-Rings (H.J. Weinert). On Subdirectly Irreducible Near-Rings which are Fields (R. Wiegandt).

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