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Compressed and Partially Compressed Zero-Divisor Graphs of Finite Associative Rings. / Afanas’ev, A. A.; Monastyreva, A. S.

In: Siberian Mathematical Journal, Vol. 64, No. 2, 03.2023, p. 291-299.

Research output: Contribution to journal › Article › peer-review

Harvard

Afanas’ev, AA & Monastyreva, AS 2023, 'Compressed and Partially Compressed Zero-Divisor Graphs of Finite Associative Rings', Siberian Mathematical Journal, vol. 64, no. 2, pp. 291-299. https://doi.org/10.1134/S0037446623020040

APA

Afanas’ev, A. A., & Monastyreva, A. S. (2023). Compressed and Partially Compressed Zero-Divisor Graphs of Finite Associative Rings. Siberian Mathematical Journal, 64(2), 291-299. https://doi.org/10.1134/S0037446623020040

Vancouver

Afanas’ev AA, Monastyreva AS. Compressed and Partially Compressed Zero-Divisor Graphs of Finite Associative Rings. Siberian Mathematical Journal. 2023 Mar;64(2):291-299. doi: 10.1134/S0037446623020040

Author

Afanas’ev, A. A. ; Monastyreva, A. S. / Compressed and Partially Compressed Zero-Divisor Graphs of Finite Associative Rings. In: Siberian Mathematical Journal. 2023 ; Vol. 64, No. 2. pp. 291-299.

BibTeX

@article{a2982690d3d24feaa2b96e68220dd106,
title = "Compressed and Partially Compressed Zero-Divisor Graphs of Finite Associative Rings",
abstract = "We study some properties of thecompressed zero-divisor graph of a finite ring andthe partially compressed zero-divisor graph of a finite nilpotent ring.In particular, we describe all nilpotent finite rings whosecompressed zero-divisor graphs are some complete graphs with loops.Furthermore, we introduce the notion of partially compressedzero-divisor graph for the nilpotent rings and study the properties of the group.Also, we describe the finite rings whose compressed zero-divisorgraph contains a bridge.",
keywords = "512.55, compressed zero-divisor graph, finite ring, nilpotent ring, partially compressed zero-divisor graph, zero-divisor",
author = "Afanas{\textquoteright}ev, {A. A.} and Monastyreva, {A. S.}",
note = "Афанасьев, А. А. Сжатые и частично сжатые графы делителей нуля конечных ассоциативных колец / А. А. Афанасьев, А. С. Монастырева // Сибирский математический журнал. – 2023. – Т. 64, № 2(378). – С. 281-291.",
year = "2023",
month = mar,
doi = "10.1134/S0037446623020040",
language = "English",
volume = "64",
pages = "291--299",
journal = "Siberian Mathematical Journal",
issn = "0037-4466",
publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",
number = "2",

}

RIS

TY - JOUR

T1 - Compressed and Partially Compressed Zero-Divisor Graphs of Finite Associative Rings

AU - Afanas’ev, A. A.

AU - Monastyreva, A. S.

N1 - Афанасьев, А. А. Сжатые и частично сжатые графы делителей нуля конечных ассоциативных колец / А. А. Афанасьев, А. С. Монастырева // Сибирский математический журнал. – 2023. – Т. 64, № 2(378). – С. 281-291.

PY - 2023/3

Y1 - 2023/3

N2 - We study some properties of thecompressed zero-divisor graph of a finite ring andthe partially compressed zero-divisor graph of a finite nilpotent ring.In particular, we describe all nilpotent finite rings whosecompressed zero-divisor graphs are some complete graphs with loops.Furthermore, we introduce the notion of partially compressedzero-divisor graph for the nilpotent rings and study the properties of the group.Also, we describe the finite rings whose compressed zero-divisorgraph contains a bridge.

AB - We study some properties of thecompressed zero-divisor graph of a finite ring andthe partially compressed zero-divisor graph of a finite nilpotent ring.In particular, we describe all nilpotent finite rings whosecompressed zero-divisor graphs are some complete graphs with loops.Furthermore, we introduce the notion of partially compressedzero-divisor graph for the nilpotent rings and study the properties of the group.Also, we describe the finite rings whose compressed zero-divisorgraph contains a bridge.

KW - 512.55

KW - compressed zero-divisor graph

KW - finite ring

KW - nilpotent ring

KW - partially compressed zero-divisor graph

KW - zero-divisor

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85151079349&origin=inward&txGid=5cf7c88b610ce7a4377121ea5dab51d7

UR - https://www.mendeley.com/catalogue/aab0cceb-81d2-318c-a673-ecbbb5a3f085/

U2 - 10.1134/S0037446623020040

DO - 10.1134/S0037446623020040

M3 - Article

VL - 64

SP - 291

EP - 299

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 2

ER -

ID: 59242907