Zero-Divisor Graphs of Matrices Over Commutative Rings

DOI10.1080/00927870802465951zbMath1185.16031OpenAlexW2108132633MaRDI QIDQ3627026

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Publication date: 14 May 2009

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

Full work available at URL: https://doi.org/10.1080/00927870802465951

zbMATH Keywords

matrix ringscommutative ringsdiameterszero-divisor graphs

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Conditions on elements (16U99)

Related Items (24)

On the zero divisor graphs of the ring of Lipschitz integers modulo \(n\) ⋮ Automorphisms of the zero-divisor graph of the ring of all \(n\times n\) matrices over a finite field ⋮ THE ZERO-DIVISOR GRAPHS OF RINGS AND SEMIRINGS ⋮ Some new results on the graph \(\Gamma_{1}(R)\) over a ring \(R\) ⋮ Square element graph of square-subtract rings ⋮ Balanced zero-divisor graphs of matrix rings. ⋮ Hamiltonian trace graph of matrices ⋮ The group of automorphisms of a zero-divisor graph based on rank one upper triangular matrices ⋮ Automorphisms of the zero-divisor graph of 2 × 2 matrix ring over ℤps ⋮ Cayley-Dickson split-algebras: doubly alternative zero divisors and relation graphs ⋮ A Note on the Uniqueness of Zero-Divisor Graphs with Loops (Research) ⋮ Unnamed Item ⋮ Automorphism group of rank-decreasing graph of matrices ⋮ A note on automorphisms of the zero-divisor graph of upper triangular matrices. ⋮ Compressed zero-divisor graphs of matrix rings over finite fields ⋮ Automorphism group of the one-divisor graph over the semigroup of upper triangular matrices ⋮ Automorphism group of an ideal-relation graph over a matrix ring ⋮ Relationship graphs of real Cayley-Dickson algebras ⋮ Automorphism Group of the Rank-decreasing Graph Over the Semigroup of Upper Triangular Matrices ⋮ Unnamed Item ⋮ On homogeneous co-maximal graphs of groupoid-graded rings ⋮ An alternative construction of graphs by associating with algorithmic approach on MV-algebras ⋮ Zero Divisor Graphs of Upper Triangular Matrix Rings ⋮ Zero Divisor Graphs of Finite Direct Products of Finite Rings

Cites Work

• Unnamed Item
• On the diameter and girth of a zero-divisor graph
• Coloring of commutative rings
• Annihilation of ideals in commutative rings
• The zero-divisor graph of a commutative ring
• Zero-divisor graphs, von Neumann regular rings, and Boolean algebras.
• On directed zero-divisor graphs of finite rings
• The diameter of a zero divisor graph
• CYCLES AND SYMMETRIES OF ZERO-DIVISORS
• Zero-Divisor Graphs of Polynomials and Power Series Over Commutative Rings

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