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Mathematical logic, algebra and number theory
On compressed zero-divisor graphs of finite commutative local rings
E. V. Zhuravlev, O. A. Filina Altai State University, 61, Lenina ave., Barnaul, 656049, Russia
Abstract:
We describe the compressed zero-divisor graphs of a commutative finite local rings $R$ of characteristic $p$ with Jacobson radical $J$ such that $J^4=(0)$, $F=R/J\cong GF(p^r)$ and ${\dim_F J/J^2=2}$, ${\dim_F J^2/J^3=2}$, ${\dim_F J^3=1}$ or ${\dim_F J/J^2=3}$, ${\dim_F J^2/J^3=1}$, ${\dim_F J^3=1}$.
Keywords:
finite ring, local ring, zero-divisor graph.
Received August 19, 2021, published December 3, 2021
Citation:
E. V. Zhuravlev, O. A. Filina, “On compressed zero-divisor graphs of finite commutative local rings”, Sib. Èlektron. Mat. Izv., 18:2 (2021), 1531–1555
Linking options:
https://www.mathnet.ru/eng/semr1459 https://www.mathnet.ru/eng/semr/v18/i2/p1531
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Abstract page: | 96 | Full-text PDF : | 37 | References: | 30 |
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