Jacobson graph construction of ring ℤ3n, for n>1

A group is called a ring if the group is a commutative under addition operation and satisfy the distributive and assosiative properties under multiplication operation. Suppose R is a commutative ring with non-zero identity, U is the unit of R, and J(R) is a Jacobson radical. Jacobson graph of a ring...

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Bibliographic Details
Published in:Journal of physics. Conference series 2020-03, Vol.1494 (1), p.12016
Main Authors: Novictor, A, Susilowati, L, Fatmawati
Format: Article
Language:English
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Summary:A group is called a ring if the group is a commutative under addition operation and satisfy the distributive and assosiative properties under multiplication operation. Suppose R is a commutative ring with non-zero identity, U is the unit of R, and J(R) is a Jacobson radical. Jacobson graph of a ring R denoted by ℑR is a graph with a vertex set is R\J(R) dan edge set is {(a, b)| 1 − ab ∉ U}. The purpose of this research is to construct a Jacobson graph of ring Z3n with n > 1. The results show that Jacobson graph of ring Z3n is a disconected graph with two components.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1494/1/012016