Master Degree / Yüksek Lisans Tezleri
Permanent URI for this collectionhttps://hdl.handle.net/11147/3008
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Master Thesis Almost Local-Global Rings(Izmir Institute of Technology, 2017) Susuzlu, İdem; Ay Saylam, BaşakThe main purpose of this thesis is to investigate the Invariant Factor Theorem for Prüfer domains. In accordance with this aim, we give a survey of necessary and su cient conditions on a Prüfer domain to satisfy the Invariant Factor Theorem. In this process, almost local-global rings have important role since they satisfy the USC-property. Regarding to the UCS-property, BCS-rings together with their properties are also investigeted.Master Thesis Krull-Schmidt Properties Over Rings of Finite Character(Izmir Institute of Technology, 2016) Gürbüz, Ezgi; Ay Saylam, BaşakThe main purpose of this thesis is to investigate the notion of Krull-Schmidt properties over rings of finite character. In accordance with this aim, we give a survey of necessary and sufficient conditions on an h-local domain for certain Krull-Schmidt properties hold for direct sums of ideals, direct sums of indecomposable submodules of finitely generated free modules and direct sums of rank one torsion-free modules. By using obtained characterizations, some useful results for Krull-Schmidt properties of modules over Noetherian and Prüfer domains are proven. Besides, the characterizations of Noetherian UDI domains are given.Master Thesis Approximation Theorems for Krull Domains(Izmir Institute of Technology, 2014) Yeşil, Mehmet; Ay Saylam, BaşakLet R be an integrally closed domain, and denote by I(R) the multiplicative group of all invertible fractional ideals of R. Let {Vi}i∈I be the family of valuation overrings of R, and denote by Gi the corresponding value group of the valuation domain Vi. We show that R = Ti∈I Vi, and there is a map from I(R) into Qi∈I Gi, the cardinal product of the Gi’s. Furthermore, it is well known when R is a Dedekind domain, this map becomes an isomorphism onto `i∈I Gi, the cardinal sum of the Gi’s. In this case, Gi ∼= Z for each i. It is shown, by J. Brewer and L. Klingler, that this map is also an isomorphism onto`i∈I Gi when R is an h-local Prüfer domain. In this thesis, we investigate the existence of such a map, and whether it is injective when R is a Krull domain.