Modular Invariants

Table of Contents

• Preface
• Part I:
• 1. A new notation
• 2. Galois fields and Fermat's theorem
• 3. Transformations in the Galois fields
• 4. Types of concomitants
• 5. Systems and finiteness
• 6. Symbolical notation
• 7. Generators of linear transformations
• 8. Weight and isobarbism
• 9. Congruent concomitants
• 10. Relation between congruent and algebraic covariants
• 11. Formal covariants
• 13. Dickson's theorem
• 14. Formal invariants of linear form
• 15. The use of symbolical operators
• 16. Annihilators of formal invariants
• 17. Dickson's method for formal covariants
• 18. Symbolical representation of pseudo-isobaric formal covariants
• 19. Classes
• 20. Characteristic invariants
• 21. Syzygies
• 22. Residual covariants
• 23. Miss Sanderson's theorem
• 24. A method of finding characteristic invariants
• 25. Smallest full systems
• 26. Residual invariants of linear forms
• 27. Residual invariants of quadratic forms
• 28. Cubic and higher forms
• 29. Relative unimportance of residual covariants
• 30. Non-formal residual covariants
• Part II:
• 31. Rings and fields
• 32. Expansions
• 33. Isomorphism
• 34. Finite expansions
• 35. Transcendental and algebraic expansions
• 36. Rational basis theorem of E. Noether
• 37. The fields Ky+/-f
• 38. Expansions of the first and second sorts
• 39. The theorem on divisor chains
• 40. R-modules
• 41. A theorem of Artin and of van der Waerden
• 42. The finiteness criterion of E. Noether
• 43. Application of E. Noether's theorem to modular covariants
• Appendix I
• Appendix II
• Appendix III
• Index.
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