On the forgotten index and Jacobson graphs associated with integer rings modulo n

Jauhari, Mohammad Nafie, Jannah, Shahnaz Latifatul, Turmudi, Turmudi and Nisfulaila, Intan (2024) On the forgotten index and Jacobson graphs associated with integer rings modulo n. KUBIK: Jurnal Publikasi Ilmiah Matematika, 9 (2). pp. 231-242. ISSN 2686-0341

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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.

Item Type:	Journal Article
Keywords:	F-Index; Jacobson Graph; Jacobson Radical; Maximal ideal; Modulo Ring.
Subjects:	01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010104 Combinatorics and Discrete Mathematics (excl. Physical Combinatorics)
Divisions:	Faculty of Mathematics and Sciences > Department of Mathematics
Depositing User:	Intan Nisfulaila
Date Deposited:	03 Dec 2024 15:04

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