NILPOTENT FINITE RINGS WITH PLANAR ZERO-DIVISOR GRAPHS

DOI10.1142/S179355710800045XzbMath1179.16007MaRDI QIDQ3622573

A. S. Kuz'mina, Yuriĭ Nikolaevich Mal'tsev

Publication date: 28 April 2009

Published in: Asian-European Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

planar graphsfinite ringsnilpotent ringszero-divisor graphs of rings

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Planar graphs; geometric and topological aspects of graph theory (05C10) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

Related Items

FINITE RINGS WITH EULERIAN ZERO-DIVISOR GRAPHS ⋮ On Nilpotent Finite Alternative Rings with Planar Zero-Divisor Graphs ⋮ Finite rings with Eulerian nilpotent graphs ⋮ Describing ring varieties in which all finite rings have Hamiltonian zero-divisor graphs. ⋮ Description of finite nonnilpotent rings with planar zero-divisor graphs ⋮ Compressed zero-divisor graphs of finite associative rings ⋮ Compressed and partially compressed zero-divisor graphs of finite associative rings ⋮ Unnamed Item ⋮ Toroidal zero-divisor graphs of decomposable commutative rings without identity ⋮ On zero-divisor graphs of commutative rings without identity ⋮ Finite rings with complete bipartite zero-divisor graphs. ⋮ On zero divisor graphs of finite commutative local rings ⋮ Finite rings with some restrictions on zero-divisor graphs.

Cites Work

• 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
• On zero-divisor graphs of finite rings.
• Planar zero-divisor graphs
• Infinite Planar Zero-Divisor Graphs
• Unnamed Item