Preface Part I. Definitions, Illustrations and Elementary Theorems: 1-2. Ordinary complex numbers, number fields 3-4. Matrices matric algebra as a linear algebra 5. Definition of linear algebras, coordinates, units 6-8. Division principal unit transformation of units 9-10. Equations and polynomials in a single number 11. Unique place of quaternions among algebras 12-13. Properties of quaternions, relation to matrices 14. Cayley's generalization of real quaternions 15-17. Characteristic determinanats invariance 18. Binary algebras 19. Rank and rank equations of an algebra 20. Ternary algebras with a modulus 21-22. Reducibility, direct sum, direct product 23-24. Units normalized relative to a number example Part II. Revision of Cartan's General Theory of Complex Linear Associative Algebras with a Modulus: 25-27. Units having a character example 28-34. Nilpotent numbers, normalized units examples 35. Separation of algebras into two categories 36-38. Algebras A1 of first category, nilpotent algebras 39. Normalized units for A1 40-45. Algebras A2 of the second category 46. Any A2 has a quaternion sub-algebra 47-48. Normalized units for A2 determinant 49. Invariant sub-algebra, simple algebras 50-51. Main theorem commutative case Part III. Relations of Linear Algebras to Other Subjects: 52. Linear associative algebras and linear groups 53. Linear associative algebras and bilinear forms 54. Relations of linear algebras and finite groups 55. Dedekind's view for commutative associative algebras Part IV. Linear Algebras over a Field F: 56. Statement of main theorem real simple algebras 57. Algebras of Weierstrass 58-60. Division algebras 61. Statement of further results 62. Analytic functions of hypercomplex numbers.
Preface Part I. Definitions, Illustrations and Elementary Theorems: 1-2. Ordinary complex numbers, number fields 3-4. Matrices matric algebra as a linear algebra 5. Definition of linear algebras, coordinates, units 6-8. Division principal unit transformation of units 9-10. Equations and polynomials in a single number 11. Unique place of quaternions among algebras 12-13. Properties of quaternions, relation to matrices 14. Cayley's generalization of real quaternions 15-17. Characteristic determinanats invariance 18. Binary algebras 19. Rank and rank equations of an algebra 20. Ternary algebras with a modulus 21-22. Reducibility, direct sum, direct product 23-24. Units normalized relative to a number example Part II. Revision of Cartan's General Theory of Complex Linear Associative Algebras with a Modulus: 25-27. Units having a character example 28-34. Nilpotent numbers, normalized units examples 35. Separation of algebras into two categories 36-38. Algebras A1 of first category, nilpotent algebras 39. Normalized units for A1 40-45. Algebras A2 of the second category 46. Any A2 has a quaternion sub-algebra 47-48. Normalized units for A2 determinant 49. Invariant sub-algebra, simple algebras 50-51. Main theorem commutative case Part III. Relations of Linear Algebras to Other Subjects: 52. Linear associative algebras and linear groups 53. Linear associative algebras and bilinear forms 54. Relations of linear algebras and finite groups 55. Dedekind's view for commutative associative algebras Part IV. Linear Algebras over a Field F: 56. Statement of main theorem real simple algebras 57. Algebras of Weierstrass 58-60. Division algebras 61. Statement of further results 62. Analytic functions of hypercomplex numbers.
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