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All Journal Semeton Mathematics Journal Perspectives in Mathematics and Applications (PERMATA)
Umam, Ashadul
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Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Engineering Mathematics Physics

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Eksplorasi Modul Noetherian Umam, Ashadul; Mifftahurrahman, Mifftahurrahman; Pratiwi, Lia Fitta
Semeton Mathematics Journal Vol 2 No 1 (2025): April
Publisher : Program Studi Matematika

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/semeton.v2i1.263

Abstract

Noetherian Modules are a fundamental concept in algebra, providing a structured framework for studying algebraic structures. These modules satisfy the ascending chain condition (ACC), which ensures that every ascending chain of submodules terminates after a finite number of steps. This article explores the definition, key properties, and applications of Noetherian modules in ring theory, homological algebra, and algebraic topology. Through this discussion, it is demonstrated that Noetherian Modules play a crucial role in analyzing ideal structures and more complex algebraic representations. The article also provides concrete examples to illustrate the properties and significance of Noetherian modules across various branches of algebra.
Analisis teoritis indeks Hyper-Wiener dalam graf yang diturunkan dari struktur aljabar Abdurahim; Umam, Ashadul
Perspectives in Mathematics and Applications Vol 1 No 02 (2025): Desember
Publisher : Kreasi Pustaka Mandiri (Krestama)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.66256/permata.v1i2.19

Abstract

The Hyper-Wiener index is a widely used topological descriptor that quantifies the structural complexity of graphs, particularly those arising from algebraic structures. This paper presents a structured synthesis of key theorems related to the Hyper-Wiener index in coprime graphs, non-coprime graphs, and power graphs constructed from the integer modulo group and the dihedral group. Adopting a systematic literature review approach, we compile and restate formal results, including explicit formulas and proven properties. Each theorem is analyzed in relation to the algebraic structure of its underlying group and the resulting graph topology. Our findings highlight how group-theoretic properties—such as order, operation, and element interactions—directly impact the Hyper-Wiener index. This paper is intended to support researchers by providing a conceptual bridge between group theory and topological graph theory, and by identifying potential directions for future work.
Co-Authors Abdurahim, Abdurahim Mifftahurrahman, Mifftahurrahman Pratiwi, Lia Fitta