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lgrsnf/Kaplansky I. An introduction to differential algebra (Hermann, 1957)(ASIN B000P26CKA)(600dpi)(T)(O)(S)(62s)_MAd_.djvu

CONTENTS
Chapter I. Generalities concerning differential rings
1. Derivations
2. Differential rings
3. Radical ideals
4. Ritt algebras
Chapter II. Extension of isomorphisms
5. Krull's theorem
6. Extension of prime ideals
7. A lemma on polynomial rings
8. Admissible isomorphisms
Chapter III. Preliminary Galois theory
9. The differential Galois group
10. The Wronskian
11. Picard-Vessiot extensions
12. Two special cases
13. Liouville extensions
14. Triangular automorphisms
Chapter IV. Algebraic matrix groups and the Zariski topology
15. Z-spaces
16. T1-groups and Z-groups
17. C-groups
18. Solvable connected matrix groups
19. A special result
Chapter V. The Galois theory
20. Three lemmas
21. Normality of Picard-Vessiot extensions
22. Completion of the Galois theory
23. Liouville extensions
Chapter VI. Equations of order two
24. The Wronskian
25. Connection with a Riccati equation
26. An example
Chapter VII. The basis theorem and applications
27. The basis theorem
28. Systems of differential equations
29. The decomposition theorem
30. Study of a single differential polynomial
31. Examples
Chapter VIII. — Appendix: more on matrix groups and their abstraction
32. Solvability
33. CZ-groups
34. Irreducible sets; the ascending chain condition
35. Images of irreducible sets
Glossary
Bibliography

2024-07-31