On the Forgotten Index and Jacobson Graphs Associated with Integer Rings Modulo n

Authors

  • Mohammad Nafie Jauhari Universitas Islam Negeri Maulana Malik Ibrahim Malang, Indonesia, Indonesia https://orcid.org/0000-0002-0909-1821
  • Shahnaz Latifatul Jannah Universitas Islam Negeri Maulana Malik Ibrahim Malang, Indonesia, Indonesia
  • Turmudi Turmudi Universitas Islam Negeri Maulana Malik Ibrahim Malang, Indonesia, Indonesia
  • Intan Nisfulaila Universitas Islam Negeri Maulana Malik Ibrahim Malang, Indonesia, Indonesia

DOI:

https://doi.org/10.15575/kubik.v9i2.39585

Keywords:

F-Index, Jacobson Graph, Jacobson Radical, Maximal ideal, Modulo Ring

Abstract

This paper investigates the connections between the Jacobson graph and the algebraic properties of rings through the analysis of the Jacobson graph of the ring \mathbb{Z}_{3p}, where p is a prime number greater than 3. The Jacobson graph of a commutative ring R is constructed by taking the elements of R, excluding its Jacobson Radical, as vertices, and connecting two distinct vertices if 1 minus their product is not a unit in R. The F-Index is utilized to capture and represent the structural properties of the ring through its associated graph. A detailed examination of the Jacobson Radical, maximal ideals, and vertex degrees in \mathbb{Z}_{3p} leads to the calculation of the F-Index, providing insights into the graph’s connectivity and underlying algebraic structure. This study contributes to the intersection of algebra and graph theory, offering a foundation for further research into more complex algebraic structures.

Author Biographies

Mohammad Nafie Jauhari, Universitas Islam Negeri Maulana Malik Ibrahim Malang, Indonesia

Program Studi Matematika

Shahnaz Latifatul Jannah, Universitas Islam Negeri Maulana Malik Ibrahim Malang, Indonesia

Program Studi Matematika

Turmudi Turmudi, Universitas Islam Negeri Maulana Malik Ibrahim Malang, Indonesia

Program Studi Matematika

Intan Nisfulaila, Universitas Islam Negeri Maulana Malik Ibrahim Malang, Indonesia

Program Studi Matematika

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Published

2024-11-30

How to Cite

Jauhari, M. N., Jannah, S. L., Turmudi, T., & Nisfulaila, I. (2024). On the Forgotten Index and Jacobson Graphs Associated with Integer Rings Modulo n. KUBIK: Jurnal Publikasi Ilmiah Matematika, 9(2), 231–242. https://doi.org/10.15575/kubik.v9i2.39585

Issue

Vol. 9 No. 2 (2024): KUBIK: Jurnal Publikasi Ilmiah Matematika

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