Minimal prime ideals and cycles in annihilating-ideal graphs

DOI10.1216/RMJ-2013-43-5-1415zbMath1276.05057MaRDI QIDQ380186

Ghodratollah Aalipour, Saieed Akbari, Farzad Shaveisi, Mohammad Javad Nikmehr, Reza Nikandish

Publication date: 13 November 2013

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1382705659

zbMATH Keywords

cyclebipartite graphannihilating-ideal graphminimal prime ideal

Mathematics Subject Classification ID

Paths and cycles (05C38) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Distribution of prime ideals (11R44) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69) Commutative Artinian rings and modules, finite-dimensional algebras (13E10)

Related Items (19)

A new graph associated to a commutative ring ⋮ The \(k\)-annihilating-ideal hypergraph of commutative ring ⋮ On the essential annihilating-ideal graph of commutative rings ⋮ The \(M\)-principal graph of a commutative ring ⋮ The projective 3-annihilating-ideal hypergraphs ⋮ A generalization of the annihilating ideal graph for modules ⋮ On a New Extension of Annihilating-Ideal Graph of Commutative Rings ⋮ On the coloring of the annihilating-ideal graph of a commutative ring ⋮ When the annihilator-ideal graph is planar or complete bipartite graph ⋮ The annihilating-submodule graph of modules over commutative rings. II ⋮ DOMINATION NUMBER IN THE ANNIHILATING-SUBMODULE GRAPH OF MODULES OVER COMMUTATIVE RINGS ⋮ Zero divisors and prime elements of bounded semirings. ⋮ Classification of rings with toroidal annihilating-ideal graph ⋮ The nil-graph of ideals of a commutative ring ⋮ On the genus of the \(k\)-annihilating-ideal hypergraph of commutative rings ⋮ The central vertices and radius of the regular graph of ideals ⋮ More on the annihilator-ideal graph of a commutative ring ⋮ Artinian Local Rings Whose Annihilating-ideal Graphs Are Star Graphs ⋮ The spectrum subgraph of the annihilating-ideal graph of a commutative ring

Cites Work

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• The clique numbers of regular graphs of matrix algebras are finite
• The total graph and regular graph of a commutative ring
• On zero-divisor graphs of small finite commutative rings
• The total graph of a commutative ring
• On bipartite zero-divisor graphs
• Zero-divisor semigroups and refinements of a star graph.
• The zero-divisor graph of a commutative semigroup
• On zero-divisor graphs of finite rings.
• THE ANNIHILATING-IDEAL GRAPH OF COMMUTATIVE RINGS I
• Commutative rings in which every proper ideal is maximal
• Intersection graphs of ideals of rings

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