| Titre : |
Compactness in modules |
| Type de document : |
texte imprimé |
| Auteurs : |
Abdallah Laradji, Auteur |
| Editeur : |
Sheffield : University of Sheffield |
| Année de publication : |
1985 |
| Importance : |
126 f. |
| Format : |
27 cm. |
| Note générale : |
Thèse de Doctorat : Mathématique Appliqués : Royaume-Uni, University of Sheffield : 1985
Annexe f. 127 - 133 . - Bibliogr. f. 134 - 136 |
| Langues : |
Anglais (eng) |
| Mots-clés : |
Mathématique Algebraic compactness Purity Pure injectivity Filters Regressive functions |
| Index. décimale : |
D002285 |
| Résumé : |
This thesis is concerned with the study of algebraic compactness for modules using systems of equations.
The first two chapters provide an introduction to the subject via purity and pure-injectivity.
In chapter 3 and 4, we discuss the various types of algebraic compactness and give some charcterizations of Σ-algebraic compact modules.
Filters are used in chaptre 5 to genrralize results on χ₀-compact quotients to higher cardinals.
In chapter 6, we show that the proof of a theorem of Mycielski on filter quotients is incorrect by using regressive functions.
The results of chapter 5 are applied to prove weaker versions of his theorem.
In the last chapter, we construct for each n Є IN a finitely solvable system of equations which is χn₋₁-solvable but not χn-solvable, and a module which is χn₋₁-compact but not χn-compact.
Finally, an appendix on ordinals and cardinals with definitions and statements of the properties used in this thesis is given. |
Compactness in modules [texte imprimé] / Abdallah Laradji, Auteur . - Sheffield : University of Sheffield, 1985 . - 126 f. ; 27 cm. Thèse de Doctorat : Mathématique Appliqués : Royaume-Uni, University of Sheffield : 1985
Annexe f. 127 - 133 . - Bibliogr. f. 134 - 136 Langues : Anglais ( eng)
| Mots-clés : |
Mathématique Algebraic compactness Purity Pure injectivity Filters Regressive functions |
| Index. décimale : |
D002285 |
| Résumé : |
This thesis is concerned with the study of algebraic compactness for modules using systems of equations.
The first two chapters provide an introduction to the subject via purity and pure-injectivity.
In chapter 3 and 4, we discuss the various types of algebraic compactness and give some charcterizations of Σ-algebraic compact modules.
Filters are used in chaptre 5 to genrralize results on χ₀-compact quotients to higher cardinals.
In chapter 6, we show that the proof of a theorem of Mycielski on filter quotients is incorrect by using regressive functions.
The results of chapter 5 are applied to prove weaker versions of his theorem.
In the last chapter, we construct for each n Є IN a finitely solvable system of equations which is χn₋₁-solvable but not χn-solvable, and a module which is χn₋₁-compact but not χn-compact.
Finally, an appendix on ordinals and cardinals with definitions and statements of the properties used in this thesis is given. |
|
D000100 
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