Abstract
We study some properties of the compressed zero-divisor graph of a finite ring and the partially compressed zero-divisor graph of a finite nilpotent ring. In particular, we describe all nilpotent finite rings whose compressed zero-divisor graphs are some complete graphs with loops. Furthermore, we introduce the notion of partially compressed zero-divisor graph for the nilpotent rings and study the properties of the group. Also, we describe the finite rings whose compressed zero-divisor graph contains a bridge.
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Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 2, pp. 281–291. https://doi.org/10.33048/smzh.2023.64.204
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Afanas’ev, A.A., Monastyreva, A.S. Compressed and Partially Compressed Zero-Divisor Graphs of Finite Associative Rings. Sib Math J 64, 291–299 (2023). https://doi.org/10.1134/S0037446623020040
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DOI: https://doi.org/10.1134/S0037446623020040
Keywords
- finite ring
- zero-divisor
- nilpotent ring
- compressed zero-divisor graph
- partially compressed zero-divisor graph