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The theory of finitely generated commutative semigroups /
The Theory of Finitely Generated Commutative Semigroups describes a theory of finitely generated commutative semigroups which is founded essentially on a single """"fundamental theorem"""" and exhibits resemblance in many respects to the algebraic theory of nu...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés Alemán |
| Publicado: |
Oxford :
Pergamon Press,
1965.
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| Edición: | First edition. |
| Colección: | International series of monographs in pure and applied mathematics ;
v. 82. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; The Theory of Finitely Generated Commutative Semigroups; Copyright page; Table of Contents; Preface; Introduction; Chapter I. Kernel functions and fundamental theorem; 1. Preliminaries; 2. Axioms I-V of the kernel functions; 3. Fundamental theorem; 4. Second form of Axiom V; 5. Proof of the fundamental theorem; Chapter II. Elementary properties of the kernel functions; 6. Set stars and ideal stars; 7. Third form of Axiom V; 8. Fourth form of Axiom V; 9. The star property of the kernel functions; 10. i'irst theorem of reciprocity; 11. Transitivity classes; 12. Reduction of Axiom V
- Chapter III. Ideal theory of free semimodules of finite rank13. Dickson's theorem; 14. The ideals of and F�; 15. Translation classes of ideals; 16. Ideal lattice and principal ideal lattice; 17. Direct decompositions in F and F�; 18. The height of ideals of F; 19. The maximal condition in the ideal lattice of 7^; 20. Semiondomorphisms of the ideal lattices of F�; 21. Certain congruences in commutative cancellative semigroups; 22. jP""-congruences by ideals; 23. Second theorem of reciprocity; 24. The classes for an ideal of F; 25. The set of classes by an ideal of F
- Chapter IV. Further properties of the kernel functions26. The kernel of -congruences or kernel functions; 27. Translated kernel functions; 28. Finiteness of the range of values of the kernel functions; 29. Classification of the kernel functions; 30. The kernel functions of first degree; 31. The enveloping kernel function of first degree; 32. The kernel functions of first order; 33. Finite definability of finitely generated commutativesemigroups; 34. The lattice of kernel functions; 35. Connection of an F-congruence with the values of thekernel function belonging to it
- 36. The submodules of F�37. Finite commutative semigroups; 38. Numerical semimodules; 39. Investigation of the kernel functions **in the little; 40. The numerical semimodules attached to the kernelfunctions; 41. The kernel functions of first rank; 42. The maximum condition in the lattice of kernel functions; 43. The normals of a kernel function; 44. Splitting kernel functions; 45. The kernel functions of second order; 46. The kernel functions of second dimension; 47. Degenerate kernel functions; Chapter V. Equivalent kernel functions
- 48. Preparations for the solution of the isomorphism problem49. Submodules of equivalent relative to F; 50. Equivalent kernel functions; Appendix; 51. The case of semigroups without a unity element; Index; Other titles in the series