Nearrings: Geneses and Applications (Oxford Science Publications)

Ch. 1. Introduction To Nearrings. 1. Getting Acquainted. 2. Lots Of Examples. 3. Many Cheerful Facts About Nearrings --^ Ch. 2. Planar Nearrings. 4. Planarity For Nearrings. 4.1. The Ferrero Planar Nearring Factory. 4.2. Output Of The Factory. 5. Construction Of Circular Planar Nearrings. 5.1. Basic Results. 5.2. New Structures From Old. 5.3. Field Generated Designs. 5.4. Ring Generated Designs. 5.5. Other Constructions. 6. Geometry Of Circular Planar Nearrings. 6.1. Equivalence Classes. 6.2. The (z[subscript Q],[actual Symbol Not Reproducible]). 6.3. Compound Closed Chains. 7. Other Geometric Structures From Planar Nearrings. 7.1. Tactical Configurations. 7.2. Karzel's Observations. 7.3. The Van Der Walt Connection. 7.4. Karzel's Hyperbolae. 7.5. The (n,b[superscript -],[actual Symbol Not Reproducible]). 7.6. Partially Balanced Incomplete Block Designs. 7.7. Double Planar Nearrings. 8. Coding, Cryptography, And Combinatorics. 8.1. Planar Nearrings And Coding Theory. 8.2. Planar Nearrings And Cryptography. 8.3. Planar Nearrings And Combinatorics. 9.^ Sharply Transitive Groups And Nondesarguesian Geometry From Planar Nearfields -- Ch. 3. The Great Unifier. 10. A Little Category Theory. 11. Group And Cogroup Objects. 12. Examples. 12.1. Example 10. 12.2. Examples 11. 12.3. Examples 12 -- Ch. 4. Some First Families Of Nearrings And Some Of Their Ideals. 13. First, What Is A Nearring Module? 14. Centralizer And Transformation Nearrings. 15. Distributively Generated Nearrings. 15.1. Endomorphism Nearrings Of Odd Generalized Dihedral Groups. 15.2. Distributively Generated Nearrings From Noncommutative Formal Group Laws. 16. The Ideals Of Abstract Affine Nearrings. 17. Polynomial Nearrings. 18. Power Series Nearrings -- Ch. 5. Some Structure Of Groups Of Units. 19. Preliminaries. 20. Direct Products In Groups Of Units. 21. Semidirect Products And Wreath Products. 22. Group Extensions With Factor Sets. 23. A Mixture Of The Above --^ Ch. 6. Avant-garde Families Of Nearrings. 24. Sandwich And Laminated Nearrings. 25. Syntactic Nearrings. 26. The Cornucopia. 26.1. Distributive Nearrings. 26.2. Matrix Nearrings. 26.3. Group Nearrings. 26.4. Meromorphic Products -- Appendix. Various Diagrams. James R. Clay. Includes Bibliographical References And Index.