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Auteur Abdallah Laradji
Documents disponibles écrits par cet auteur
Affiner la rechercheCompactness in modules / Abdallah Laradji
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 - 136Langues : 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.Exemplaires
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