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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 465–480 (Mi semr1071)  

Mathematical logic, algebra and number theory

On zero divisor graphs of finite commutative local rings

E. V. Zhuravlev, A. S. Monastyreva

Altai State University, 61, Lenina ave., Barnaul, 656049, Russia

Abstract: We describe the zero divisor graph of a commutative finite local rings $R$ of characteristic $2$ with Jacobson radical $J$ such that ${\dim_F J/J^2=2}$, ${\dim_F J^2/J^3=2}$, ${\dim_F J^3=1}$, $J^4=(0)$ and $F=R/J\cong GF(2^r)$, the finite field of $2^r$ elements.

Keywords: finite ring, local ring, zero divisor graph.

DOI: https://doi.org/10.33048/semi.2019.16.029

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Bibliographic databases:

UDC: 512.55
MSC: 16P10
Received March 26, 2018, published April 2, 2019

Citation: E. V. Zhuravlev, A. S. Monastyreva, “On zero divisor graphs of finite commutative local rings”, Sib. Èlektron. Mat. Izv., 16 (2019), 465–480

Citation in format AMSBIB
\Bibitem{ZhuMon19}
\by E.~V.~Zhuravlev, A.~S.~Monastyreva
\paper On zero divisor graphs of finite commutative local rings
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 465--480
\mathnet{http://mi.mathnet.ru/semr1071}
\crossref{https://doi.org/10.33048/semi.2019.16.029}


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