Flat örtüler ve genelleştirilmiş tam halkalar
Flat covers and generalized perfect rings
- Tez No: 244838
- Danışmanlar: PROF. DR. DERYA KESKİN TÜTÜNCÜ
- Tez Türü: Yüksek Lisans
- Konular: Matematik, Mathematics
- Anahtar Kelimeler: Flat module, flat cover, G?perfect ring, max ring, perfect ring
- Yıl: 2009
- Dil: Türkçe
- Üniversite: Hacettepe Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Matematik Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 56
Özet
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Özet (Çeviri)
This thesis consists of three chapters. The first chapter, contains the preinformationwhich is necessary for the thesis.Let M be a module. A projective cover of M is the epimorphism f : P ¡! Mwhere PR is projective and Ker(f) ¿ P. Let R be a ring. If all right (left) R?modules have projective cover, Bass defined the ring R as right (left) perfect ring.For a module M, if the projective module P in the Bass?s projective cover definitionis replaced by the flat module, then the module P is called a flat cover of M (*). Ifall right (left) R?modules have flat covers, then R is called right (left) generalizedperfect (G-perfect) ring. As an equivalent condition to the Bass?s projective coverdefinition, the projective cover of M is the homomorphism à : P ¡! M such that;(i) P is a projective R?module.(ii) For any homomorphism ' : P0 ¡! M, where P0 is a projective R?module, thereis ¹ : P0 ¡! P such that à ± ¹ = '.(iii) If ¸ : P ¡! P is an endomorphism of P such that à ± ¸ = Ã, then ¸ is anautomorphism.Inspired by this characterization, in 1981 Enochs defined the flat cover by takingthe projective modules P and P0 in the above definition as flat modules. In 2001Bican, El Bashir ve Enochs have been proved that all modules have flat covers in thesense of Enochs. However any module may not have a flat cover in the sense of (*).In the second chapter of the thesis, examples are given both for modules which haveflat covers and do not have flat covers in the sense of (*) and right (left) G-perfectrings are investigated. Also commutative G-perfect rings are considered.In the third chapter of the thesis, some classes of modules which have flat coversinvestigated. The conditions under which the submodules of a module has a flatcover are investigated.
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