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All Journal EIGEN MATHEMATICS JOURNAL Semeton Mathematics Journal IJASDS: Indonesian Journal of Applied Statistics and Data Science
Luzianawati, Luzianawati
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Journal : semeton mathematics journal

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Analisis Submodul dan Sifat Keprimaan dalam Ruang Modul Musyarrofah, Sefti Fajriatul; Karang, I Gusti Yogananda; Hisan, Khairatun; Luzianawati, Luzianawati
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.v2i1.262

Abstract

This study analyzes prime submodules and primality properties in module spaces, fundamental topics in abstract algebra. The primary objective is to determine conditions for prime submodule formation in commutative rings and to examine their relationship with nearly prime submodules. The approach employed involves the decomposition of modules in principal ideal domains, with particular attention given to the concepts of annihilators, submodule orders, and the characteristics of torsion-free quotient modules. The findings indicate that nearly prime submodules can only be regarded as prime submodules in free modules. Furthermore, the module decomposition approach proves effective for gaining a comprehensive understanding of module structures. The concepts of annihilators and submodule orders provide profound insights into the relationships between module elements and ring elements. This study offers significant theoretical contributions to abstract algebra and establishes a foundation for further developments, particularly in applications related to number theory and cryptography.
Indeks Harary Graf Koprima dan Graf Pangkat pada Grup Bilangan Bulat Modulo serta Grup Dihedral Luzianawati, Luzianawati; Satriyantara, Rio
Semeton Mathematics Journal Vol 2 No 2 (2025): Oktober
Publisher : Program Studi Matematika

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/semeton.v2i2.307

Abstract

This study investigates the Harary Index of coprime graphs and power graphs constructed from the integer modulo group and the dihedral group. A coprime graph is defined as a graph whose vertices represent the elements of a group, where two vertices are adjacent if the orders of the corresponding elements are relatively prime. Meanwhile, a power graph is a graph in which two elements are connected whenever one is a power of the other within the group. The Harary Index is employed to measure the topological characteristics of the graph based on the distances between its vertices. The results show that the structure of the generated graphs allows for an explicit computation of the Harary Index, particularly for groups whose orders are prime powers.graphs facilitate the calculation of the Harary Index , especially for groups with prime power order.
Co-Authors Harsyiah, Lisa Hidayat, Muhammad Ahsan Hisan, Khairatun I Gede Adhitya Wisnu Wardhana Karang, I Gusti Yogananda Musyarrofah, Sefti Fajriatul Ningrum, Salsabila Hadi Putri Ramdhani, Triana Putri Rio Satriyantara Tri Dharmayani, Ni Komang Zindawi, M. Daffa Rizki