Non-Jordaness of the automorphism group of the zero-divisor graph of a matrix ring over number rings

Won Tae Hwang; Ei Thu Thu Kyaw

doi:10.1016/j.indag.2026.04.002

Non-Jordaness of the automorphism group of the zero-divisor graph of a matrix ring over number rings

Won Tae Hwang
, Ei Thu Thu Kyaw^*

^*Corresponding author for this work

Department of Mathematics

Yonsei University

Research output: Contribution to journal › Journal article › peer-review

Abstract

We provide a construction of the induced subgraphs of the zero-divisor graph of M₂(R) for the ring R of algebraic integers of some number fields that are neither complete nor connected, and study the structure of the induced subgraphs explicitly. As an application, we prove that the automorphism group of the zero-divisor graph of M₂(R) is not a Jordan group.

Original language	English
Journal	Indagationes Mathematicae
DOIs	https://doi.org/10.1016/j.indag.2026.04.002
State	Accepted/In press - 2026

Keywords

Automorphism group of a graph
Jordan property of a group
Twisted cubic curve
Zero-divisor graph

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10.1016/j.indag.2026.04.002

Cite this

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title = "Non-Jordaness of the automorphism group of the zero-divisor graph of a matrix ring over number rings",

abstract = "We provide a construction of the induced subgraphs of the zero-divisor graph of M2(R) for the ring R of algebraic integers of some number fields that are neither complete nor connected, and study the structure of the induced subgraphs explicitly. As an application, we prove that the automorphism group of the zero-divisor graph of M2(R) is not a Jordan group.",

keywords = "Automorphism group of a graph, Jordan property of a group, Twisted cubic curve, Zero-divisor graph",

author = "Hwang, \{Won Tae\} and Kyaw, \{Ei Thu Thu\}",

note = "Publisher Copyright: {\textcopyright} 2026 Royal Dutch Mathematical Society (KWG).",

year = "2026",

doi = "10.1016/j.indag.2026.04.002",

language = "English",

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TY - JOUR

T1 - Non-Jordaness of the automorphism group of the zero-divisor graph of a matrix ring over number rings

AU - Hwang, Won Tae

AU - Kyaw, Ei Thu Thu

PY - 2026

Y1 - 2026

N2 - We provide a construction of the induced subgraphs of the zero-divisor graph of M2(R) for the ring R of algebraic integers of some number fields that are neither complete nor connected, and study the structure of the induced subgraphs explicitly. As an application, we prove that the automorphism group of the zero-divisor graph of M2(R) is not a Jordan group.

AB - We provide a construction of the induced subgraphs of the zero-divisor graph of M2(R) for the ring R of algebraic integers of some number fields that are neither complete nor connected, and study the structure of the induced subgraphs explicitly. As an application, we prove that the automorphism group of the zero-divisor graph of M2(R) is not a Jordan group.

KW - Automorphism group of a graph

KW - Jordan property of a group

KW - Twisted cubic curve

KW - Zero-divisor graph

UR - https://www.scopus.com/pages/publications/105036861472

U2 - 10.1016/j.indag.2026.04.002

DO - 10.1016/j.indag.2026.04.002

M3 - Journal article

AN - SCOPUS:105036861472

SN - 0019-3577

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

ER -

Non-Jordaness of the automorphism group of the zero-divisor graph of a matrix ring over number rings

Abstract

Keywords

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