Master Degree / Yüksek Lisans Tezleri

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

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Language: search.filters.language.enSubject: search.filters.subject.Rings (Algebra)

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Now showing 1 - 7 of 7
  • Master Thesis
    On the Rings Whose Injective Modules Are Max-Projective
    (01. Izmir Institute of Technology, 2023) Yurtsever, Haydar Baran; Büyükaşık, Engin; Büyükaşık, Engin
    In this thesis, for some classes of rings including, local, semilocal right semihereditary and right Noetherian right nonsingular, we obtain some conditions that equivalent to being right max-QF. For example, for a semilocal right semihereditary ring, we prove that, the ring is right max-QF if and only if it is a direct product of a semisimple ring and a right small ring. A right Noetherian right nonsingular ring is right max-QF if and only if every injective module can be expressed as a direct sum of an injective module with no maximal submodules and a projective module. We show that, for a ring, being max-QF and almost-QF are not left-right symmetric. An example is given in order to show that max-QF and almost-QF rings are not closed under factor rings.
  • Master Thesis
    Almost Local-Global Rings
    (Izmir Institute of Technology, 2017) Susuzlu, İdem; Ay Saylam, Başak
    The 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, 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.
  • Master Thesis
    Semiperfect and Perfect Group Rings
    (Izmir Institute of Technology, 2014) Kalaycı, Tekgül; Pusat, Dilek
    In this thesis, we give a survey of necessary and sufficient conditions on a group G and a ring R for the group ring RG to be semiperfect and perfect. A ring R is called semiperfect R/RadR is semisimple and idempotents of R/RadR can be lifted to R. It is given that if RG is semiperfect, so is R. Necessary conditions on G for RG to be semiperfect are also given for some special type of groups. For the sufficient conditions, several types of rings and groups are considered. If R is commutative and G is abelian, a complete characterization is given in terms of the polynomial ring R[X]. A ring R is called left (respectively, right) perfect if R/Rad R is semisimple and Rad R is left (respectively, right) T-nilpotent. Equivalently, a ring is called left (respectively, right) perfect if R satisfies the descending chain condition on principal right (respectively, left) ideals. By using these equivalent definitions of a perfect ring and results from group theory, a complete characterization of a perfect group ring RG is given in terms of R and G.
  • Master Thesis
    On δ-perfect and δ-semiperfect rings
    (Izmir Institute of Technology, 2014) Kızılaslan, Gonca; Pusat, Dilek
    In this thesis, we give a survey of generalizations of right-perfect, semiperfect and semiregular rings by considering the class of all singular R-modules in place of the class of all R-modules. For a ring R and a right R-module M, a submodule N of M is said to be δ-small in M if, whenever N +X = M with M / X singular, we have X = M. If there exists an epimorphism p : P → M such that P is projective and Ker(p) is δ-small in P, then we say that P is a projective δ-cover of M. A ring R is called δ-perfect (respectively, δ-semiperfect) if every R-module (respectively, simple R-module) has a projective δ-cover. In this thesis, various properties and characterizations of δ-perfect and δ-semiperfect rings are stated.
  • Master Thesis
    Totally Weak Supplemented Modules
    (Izmir Institute of Technology, 2007) Top, Serpil; Alizade, Rafael
    The main purpose of this thesis is to give a survey about some classes of modules including supplemented, weakly supplemented, totally supplemented and totally weak supplemented modules over commutative Noetherian rings, in particular over Dedekind domains based on results of H. Zöschinger, P. Rudlof and P. F. Smith. A module is weakly supplemented if and only if the factor of that module by a finite direct sum of its hollow submodules is weakly supplemented. A module is weakly supplemented (totally weak supplemented) if and only if the factor of it by a linearly compact submodule is weakly supplemented (totally weak supplemented).
  • Master Thesis
    On pseudo semisimple rings
    (Izmir Institute of Technology, 2013) Mutlu, Hatice; Büyükaşık, Engin; Büyükaşık, Engin
    In this thesis, we give a survey of right pseudo semisimple rings and prove some new results about these rings. Namely, we prove that a right pseudo semisimple ring is an internal exchange ring and a right pseudo semisimple ring is an SSP ring. We also give a complete characterization of right and left pseudo semisimple rings.