Zayıf Asal Alt Modüller

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Thesis Type: Postgraduate

Institution Of The Thesis: Yıldız Technical University, Graduate School of Natural and Applied Sciences, MATEMATİK ANABİLİM DALI, Turkey

Approval Date: 2023

Thesis Language: Turkish

Student: YASEMİN ŞİMŞEK

Supervisor: Gürsel Yeşilot

Open Archive Collection: AVESIS Open Access Collection

Abstract:

This thesis consists of 5 chapters. Throughout this thesis, all R rings mentioned, unless otherwise stated, are assumed to be unitary and commutative. In the introduction of this thesis, the summary of the literature review, the purpose of the thesis and the hypothesis are presented. In the second chapter, which is the preliminaries section, the necessary basic algebraic knowledge for the comprehensibility of the study is given under the subheadings: Rings and Ideals; Ring Homomorphisms; Maximal, Prime and Primary Ideals; Properties of Prime and Weakly Prime Ideals; Modules and Submodules. In the third chapter of the study, prime submodules are examined with their basic definitions and properties. The main chapter of the thesis, the fourth chapter, introduces the concept of weakly prime submodules and discusses the similarities and differences between prime and weakly prime submodules, as well as the properties of weakly prime submodules of multiplication modules.