Let $ R $ be a ring with identity. The commuting graph of $ R $ is the graph associated to $ R $ whose vertices are non-central elements in $ R $, and distinct vertices $ A $ and $ B $ are adjacent if and only if $ AB = BA $. In this paper, we completely determine the automorphism group of the commuting graph of $ 2\times 2 $ matrix ring over $ \mathbb{Z}_{p^{s}} $, where $ \mathbb{Z}_{p^{s}} $ is the ring of integers modulo $ p^{s} $, $ p $ is a prime and $ s $ is a positive integer.

Autor:	Hengbin Zhang
Jazyk:	angličtina
Rok vydání:	2021
Předmět:	commuting graph automorphism group matrix ring Mathematics QA1-939
Zdroj:	AIMS Mathematics, Vol 6, Iss 11, Pp 12650-12659 (2021)
Druh dokumentu:	article
ISSN:	2473-6988
DOI:	10.3934/math.2021729?viewType=HTML
Popis:	Let $ R $ be a ring with identity. The commuting graph of $ R $ is the graph associated to $ R $ whose vertices are non-central elements in $ R $, and distinct vertices $ A $ and $ B $ are adjacent if and only if $ AB = BA $. In this paper, we completely determine the automorphism group of the commuting graph of $ 2\times 2 $ matrix ring over $ \mathbb{Z}_{p^{s}} $, where $ \mathbb{Z}_{p^{s}} $ is the ring of integers modulo $ p^{s} $, $ p $ is a prime and $ s $ is a positive integer.
Databáze:	Directory of Open Access Journals
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