On zero divisor graphs of finite commutative local rings

DOI10.33048/semi.2019.16.029zbMath1423.13037OpenAlexW3015852553MaRDI QIDQ2003250

Anna Sergeevna Monastyreva, Evgeniĭ Vladimirovich Zhuravlev

Publication date: 16 July 2019

Published in: Sibirskie Èlektronnye Matematicheskie Izvestiya (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.33048/semi.2019.16.029

zbMATH Keywords

local ringfinite ringzero divisor graph

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Ideals and multiplicative ideal theory in commutative rings (13A15)

Cites Work

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• The description of varieties of rings whose finite rings are uniquely determined by their zero-divisor graphs.
• On some properties of ring varieties in which finite rings are uniquely determined by their zero-divisor graphs.
• Coloring of commutative rings
• The zero-divisor graph of a commutative ring
• When a zero-divisor graph is planar or a complete \(r\)-partite graph
• Rings of order \(p^5\). I: Nonlocal rings
• Rings of order \(p^5\). II: Local rings
• Planar zero-divisor graphs
• Zero-divisor graphs of non-commutative rings.
• Unit groups of cube radical zero commutative completely primary finite rings
• On the classification of finite commutative local rings
• FINITE RINGS WITH EULERIAN ZERO-DIVISOR GRAPHS
• Local Rings with Genus Two Zero Divisor Graph
• NILPOTENT FINITE RINGS WITH PLANAR ZERO-DIVISOR GRAPHS
• Classification of Finite Rings of Order p²
• The Zero Divisor Graphs of Commutative Local Rings of Orderp⁴andp⁵
• The zero divisor graphs of finite rings of cubefree order

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