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Geometry of Derivation, Volume II: Theory of Skewfield Flocks book cover

1st Edition

Geometry of Derivation, Volume II Theory of Skewfield Flocks

By Norman L. Johnson Copyright 2026
340 Pages
by Chapman & Hall

This book is concerned mainly with the theory of flocks over skewfields. It begins with discussing what conditions would be required to find a possible way to extend flocks of hyperbolic quadrics and flocks of quadratic cones. This theory completely changes the idea of derivation of an affine plane that contains a derivable net. This volume will give the necessary theory for the reader to... Read more

Part 1: When Quasifibrations become Spreads

1. Quasifibrations

2. Unwrapping

3. Twisted Extensions

4. Semifield Planes from Cyclic Algebras

5. Proper Quasifibrations of Dimension 2

Part 2:  Skewfield Flocks-A Window

6. The Main Points and Ideas

Part 3: Foundations of Flock Theory

7. Building the Foundation

8. Generic and Non-Generic Flocks

Part 4: Framework for Flock Theory

9. Setting up Flock and Spread Connections

Part 5: Left σ−A Flocks and Spreads

10. Left σ − A-Hyperbolic Flocks

11. Left σ − A-Conical Flocks; 1st and 2nd Main Theorems

12. The Lower Left Form Theory

13. The 1st General Theorem of Flocks over Skewfields

Part 6: Right τ − A∗ Flocks and Spreads

14. τ − A∗ Hyperbolic Flocks

15. Right τ − A∗ Hyperbolic 1st and 2nd Main Theorems

16. τ − A∗ Right Conical Flocks

17. The Right Upper Form Theory

18. Four “Easy” Problems

Part 7: The Kaleidoscope of Derivable Nets

19. The Conical and Hyperbolic Isomorphism Questions

Part 8: Apps of the Kaleidoscope

20. Resolution and Return-Flock Spreads

21. A Class of Linear 1 − Cc−Conical Flocks

Part 9: Double Covers

22. The Left Generic Elation Double Nets

Part 10: The Group of Conical Flock Spreads

23. Why Semifields?

24. Omnibus Theorem

Part 11: Quaternion Division Ring Variations

25. 1-A Left Conical Spreads

26. Why Unwrapping?

Part 12: Left Pseudo-Regulus-Inducing Homology Groups and Transposition

27. Inversing-Right Hyperbolic Spreads

Biography

Norman L. Johnson is an Emeritus Professor (2011) at the University of Iowa where he has had ten PhD students. He received his Ph.D. at Washington State University as a student of T.G. Ostrom. He has written 580 research items including articles, books, and chapters available on Researchgate.net. Additionally, he has worked with approximately 40 coauthors and is a previous Editor for International Journal of Pure and Applied Mathematics and Note di Matematica. Dr. Johnson plays ragtime piano and enjoys studying languages and 8-ball pool.

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