The Zero Divisor Graphs of Commutative Local Rings of Orderp4andp5

DOI10.1080/00927872.2011.635619zbMath1262.05077OpenAlexW2090538844MaRDI QIDQ4916431

Nathan Bloomfield

Publication date: 22 April 2013

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927872.2011.635619

zbMATH Keywords

Finite commutative ringFinite local ringZero divisor graph

Mathematics Subject Classification ID

Enumeration in graph theory (05C30) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Structure of finite commutative rings (13M05)

Related Items (8)

On compressed zero-divisor graphs of finite commutative local rings ⋮ The compressed zero-divisor graphs of order 4 ⋮ Compressed zero-divisor graphs of finite associative rings ⋮ Compressed and partially compressed zero-divisor graphs of finite associative rings ⋮ Finite non-nilpotent rings with complete compressed zero-divisor graphs ⋮ Associate class graph of zero-divisors of a commutative ring ⋮ On zero divisor graphs of finite commutative local rings ⋮ THE ZERO-DIVISOR GRAPH OF A MODULE

Cites Work

• Zero-divisor graphs of genus one
• Coloring of commutative rings
• The zero-divisor graph of a commutative ring
• Rings of order \(p^5\). I: Nonlocal rings
• Rings of order \(p^5\). II: Local rings
• Planar zero-divisor graphs
• The graph genus problem is NP-complete
• Local Rings with Genus Two Zero Divisor Graph
• Classification of Rings with Genus One Zero-Divisor Graphs

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