Yazar "Mekera, Rasie" seçeneğine göre listele

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    Öğe
    A Generalization of Source of Semiprimeness
    (Naim ÇAĞMAN, 2024) Camcı, Didem Karalarlıoğlu; Yeşil, Didem; Mekera, Rasie; Camcı, Çetin
    This paper characterizes the semigroup ideal $\mathcal{L}_{R}^{n}(I)$ of a ring $R$, where $I$ is an ideal of $R$, defined by $\mathcal{L}_{R}^{0}(I)=I$ and $\mathcal{L}_{R}^{n}(I)=\{a\in R \mid aRa\subseteq \mathcal{L}_{R}^{n-1}(I)\}$, for all $n\in \mathbb{Z}^+$, the set of all the positive integers. Moreover, it studies the basic properties of the set $\mathcal{L}_{R}^{n}(I)$ and defines $n$-prime ideals, $n$-semiprime ideals, $n$-prime rings, and $n$-semiprime rings. This study also investigates relationships between the sets $\mathcal{L}_{R}(I)$ and $\mathcal{L}_{R}^{n}(I)$ and exemplifies some of the related properties. It obtains the main results concerning prime rings and prime ideals by the properties of the set $\mathcal{L}_{R}^{n}(I)$.
  • [ X ]
    Öğe
    A Generalization of the Prime Radical of Rings
    (Izmir University of Democracy, 2023) Camcı, Didem Karalarlıoğlu; Yeşil, Didem; Mekera, Rasie; Camcı, Çetin
    Let $R$ be a ring, $I$ be an ideal of $R$, and $\sqrt{I}$ be a prime radical of $I$. This study generalizes the prime radical of $\sqrt{I}$ where it denotes by $\sqrt[n+1]{I}$, for $n\in \mathbb{Z}^{+}$. This generalization is called $n$-prime
  • Küçük Resim
    Öğe
    A Source of Semiprimeness on Inverse and Completely Regular Semigroups
    (Springer, 2025) Mekera, Rasie; Yeşil, Didem
    We define |SS|-inverse semigroup and |SS|-completely regular semigroup structures that are not encountered in the literature. They are studied in our work for the first time. The properties of these new semigroup types and their relations with the other semigroup types, such as |SS|-idempotent, |SS|-regular, |SS|-nonzero, and |SS|-reduced semigroups, are discussed. Furthermore, the relationship between the source of semiprimeness and the semiprime ideal is analyzed. It is also shown that the intersection of all semiprime ideals is equal to the source of semiprimeness. Moreover, if a function is surjective, then it can be shown that the analyzed two structures are preserved under homomorphism.
  • [ X ]
    Öğe
    The Source of ?-Primeness on ?-Rings
    (Murat TOSUN, 2024) Yeşil, Didem; Mekera, Rasie
    The source of the primeness texture is a skeleton that generalizes traditional prime rings. In this context, our primary aim in this study is to describe the source of ?-primeness in ?-rings not included in the literature. This work’s purpose is to generalize the concept of the source of primeness to a ?-ring. In this study, the characteristics provided by the defined concept are also discussed, and the results achieved are exemplified. © MSAEN.
  • Küçük Resim
    Öğe
    Yarıgrup çeşitlerinde yarıasallığın kaynağı
    (Çanakkale Onsekiz Mart Üniversitesi, Lisansüstü Eğitim Enstitüsü, 2022) Mekera, Rasie; Yeşil, Didem
    Bu çalışmada, verilen çeşitli S yarıgrupları için SS = {a ∈ S | aSa = (0)} biçiminde tanımlanan yarıasallıgın kaynağı kümesinin bazı özellikleri incelenecektir. Bu çalışmanın amacı, matematigin ve özellikle cebirin önemli konularından biri olan yarıgrup teorisinde elde edilecek genellemeler ve bağlantılar ile problemlere etkili çözümler getirmektir. Ayrıca bu konunun yarıgrup çeşitlerinde araştırılması hem literatüre yeni tanım ve problemler ekleyecek hem de halka teorisi ile yarıgrup teorisi arasında ilişkiler kurulmasına yardımcı olacaktır.