Modular Invariants Cambridge Tracts in Mathematics Series

Originally published in 1932 as number twenty=seven in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides a concise account of the theory of modular invariants as embodied in the work of Dickson, Glenn and Hazlett. Appendices are included. This book will be of value to anyone with an interest in modular invariants and the history of mathematics.

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.