Master Degree / Yüksek Lisans Tezleri

Permanent URI for this collectionhttps://hdl.handle.net/11147/3008

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Institution Author: search.filters.institutionAuthor.Gürbüz, EzgiSubject: search.filters.subject.Modules (Algebra)

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  • Master Thesis
    Krull-Schmidt Properties Over Rings of Finite Character
    (Izmir Institute of Technology, 2016) Gürbüz, Ezgi; Ay Saylam, Başak
    The 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.