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https://hdl.handle.net/11147/4176
Title: | Approximation theorems for Krull domains | Other Titles: | Krull tamlık bölgeleri için yaklaşım teoremleri | Authors: | Yeşil, Mehmet | Advisors: | Ay Saylam, Başak | Keywords: | Krull domains Approximation theorms |
Publisher: | Izmir Institute of Technology | Abstract: | Let 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. | Description: | Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2014 Includes bibliographical references (leaves: 29) Text in English; Abstract: Turkish and English vii, 29 leaves |
URI: | http://hdl.handle.net/11147/4176 |
Appears in Collections: | Master Degree / Yüksek Lisans Tezleri |
Files in This Item:
File | Description | Size | Format | |
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10035456.pdf | MasterThesis | 195.5 kB | Adobe PDF | View/Open |
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