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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.
- Source :
- AIMS Mathematics, Vol 6, Iss 11, Pp 12650-12659 (2021)
- Publication Year :
- 2021
- Publisher :
- AIMS Press, 2021.
-
Abstract
- 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.
- Subjects :
- commuting graph
automorphism group
matrix ring
Mathematics
QA1-939
Subjects
Details
- Language :
- English
- ISSN :
- 24736988
- Volume :
- 6
- Issue :
- 11
- Database :
- Directory of Open Access Journals
- Journal :
- AIMS Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.611485b5bb145638982a7c5ccf1c634
- Document Type :
- article
- Full Text :
- https://doi.org/10.3934/math.2021729?viewType=HTML