Alizade, Refail
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01.01.02.02. Matematik Bölümü
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Master Thesis Solution Methods of Olimpiads Problems on Functions(2017) Uzun, Murat; Alizade, RefailIn this study functions are discussed starting from the high scool level. The general and private solutions of functional equations are investigated. Some spesific functional equations are described in detail. Besides questions and solutions about functional equations which asked before in National and International Mathematical Olimpiads are given. We hope that this thesis will be helpfull for high school students that take part in the mathematical olympiads.Doctoral Thesis Saf projektif fakir modüller(2019) Sipahi, Damla Dede; Alizade, RefailIn this thesis, (pure-) projective poor modules and p-impecunious modules are studied. Modules with pure projectivity domain equal to the class of pure split modules are called pureprojective poor modules (pp-poor); modules whose projectivity domain is equal to the class of semisimple modules are called projective poor modules (p-poor); modules whose projectivity domain is contained in the class of all pure split modules are called p-impecunious modules. It is shown that poor abelian groups and p-poor abelian groups coincide. Over Von Neumann regular ring, class of p-poor modules, pp-poor modules and p-impecunious modules are the same. The rings over which every right R-modules is p-impecunious are described. It is shown that abelian group A is p-impecunious if and only if Tp(A)≠0 for every prime number p. The rings over which every right R-modules is pp-poor rings are described. Let Mod-R be the class of all modules, I be the class of all injective modules, AP be the class of all absolutely pure modules and Ꭓ={X| Ext1(X;A) = 0 for every A ∈ AP}. It is shown that if there is a pp-poor module X from Ꭓ, then R is noetherian and all modules are in Ꭓ. It is proved that ⊕Ri, where {Ri}, i∈I is the set of all rational group is pp-poor group and there is no pp-poor group.Master Thesis Dıyofant denklemler(2017) Güllü, Ali Can; Alizade, RefailBu çalı¸smada; Diyofant denklemlerinin genel ve özel çözüm yöntemleri ele alınmı¸s, bazı özel diyofant denklemlerinin çözümleri verilmi¸stir. Ayrıca ulusal ve uluslararası matematik olimpiyatlarında diyofant denklemler ile ilgili çıkmış sorular ve çözümleri verilmiştir. Tezin matematik olimpiyatlarına hazırlanan öğrenciler ve bunları çalıştıracak öğretmenler için faydalı olacağı düsünülmektedir. Anahtar sözcükler: Diyofant Denklemler, Pell Penklemleri, Pisagor Üçlüleri, Fermat Teoremi, Vieta Jumping, Fermat'ın Sonsuz İndirgeme MetoduDoctoral Thesis Minimum sağ ideallere bağlı saflık(2022) Sağbaş, Selçuk; Alizade, RefailThe proper classes that are flatly, injectively and projectively generated by simple modules coincide over the ring of integers. These three classes are distinct from each other, in general. Therefore each of these classes and their homological objects are studied independently. In this Ph.D. thesis, we investigate the proper classes that are flatly and projectively generated by minimal right ideals. We study the coinjective and coprojective objects of these classes respectively. These objects are termed as weakly absolutely s-pure and weakly neat-flat, respectively. Certain rings that are characterized via these modules are investigated. The rings whose weakly neat-flat (resp. weakly absolutely s-pure) modules satisfy certain conditions, such as being neat-flat (resp. absolutely s-pure), injective, projective, nonsingular or flat are studied. For instance, it is proved that R is a right Kasch ring if and only if every weakly neat-flat right R-module is neat-flat (moreover if R is right min-coherent) if and only if every weakly absolutely s-pure left R-module is absolutely s-pure. The rings over which every right weakly neat-flat (resp. weakly absolutely s-pure) module is injective and projective are exactly the QF rings. For a commutative Noetherian ring, we prove that, every cyclic weakly neat-flat module is projective if and only if the ring is QF. We also study enveloping and covering properties of weakly absolutely s-pure and weakly neat-flat modules. The rings over which every simple right ideal has an epic projective envelope are characterized. In addition, we investigate weakly singly-injective and weakly C-flat modules which are obtained by considering principal right ideals instead of minimal right ideals. Certain rings are characterized by means of these modules. We also consider enveloping and covering properties of weakly singly-injective and weakly C-flat modules.Master Thesis İçerme dışarma prensibi(2019) Eren, Onur; Alizade, RefailIn this thesis, it has shown that how to apply the inclusion and exclusion principle for solving mathematical problems. Also it includes national and international mathematical olympiads questions and their solutions about the inclusion and exclusion principle. It is thought that this thesis will be helpful for students who are preparing for the mathematical olympiads and their teachers.
