Zero-divisor graphs of amalgamated duplication of a ring along an ideal

DOI10.1016/j.jpaa.2007.05.015zbMath1149.13001arXivmath/0701631OpenAlexW2027797941MaRDI QIDQ2456392

Hamid Reza Maimani, Siamak Yassemi

Publication date: 18 October 2007

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701631

zbMATH Keywords

zero-divisor graphamalgamated duplicationdiameter of a graphgirth of a graph

Mathematics Subject Classification ID

Structural characterization of families of graphs (05C75) Ideals and multiplicative ideal theory in commutative rings (13A15)

Related Items (28)

On the Comaximal (Ideal) Graph Associated With Amalgamated Algebra ⋮ A note on zero-divisor graph of amalgamated duplication of a ring along an ideal ⋮ Prüfer property in amalgamated algebras along an ideal ⋮ Associated prime ideals of the amalgamated algebra ⋮ Homological dimensions of the amalgamated duplication of a ring along a pure ideal ⋮ Hilbert rings and G(oldman)-rings issued from amalgamated algebras ⋮ A Survey on Algebraic and Homological Properties of Amalgamated Algebras of Commutative Rings ⋮ Bi-amalgamations subject to the arithmetical property ⋮ Gorenstein global dimension of an amalgamated duplication of a coherent ring along an ideal ⋮ The amalgamated duplication of a ring along a multiplicative-canonical ideal ⋮ The zero-divisor graph of an amalgamated algebra ⋮ The graph of zero-divisors of quadratic quotients of Rees algebras ⋮ On strong \((A)\)-rings ⋮ THE IDEALS OF AN IDEAL EXTENSION ⋮ Properties of chains of prime ideals in an amalgamated algebra along an ideal ⋮ Unnamed Item ⋮ On an amalgamated duplication of a ring along an ideal which are quasi-Frobenius ⋮ New Algebraic Properties of an Amalgamated Algebra Along an Ideal ⋮ Prüfer conditions in amalgamated algebras ⋮ Ring and Semigroup Constructions ⋮ Radical factorization for trivial extensions and amalgamated duplication rings ⋮ The diameter of the zero-divisor graph of an amalgamated algebra ⋮ A Family of Quotients of the Rees Algebra ⋮ Prüfer Conditions in an Amalgamated Duplication of a Ring Along an Ideal ⋮ SELF INJECTIVE AMALGAMATED DUPLICATION OF A RING ALONG AN IDEAL ⋮ Unnamed Item ⋮ CLEANNESS AND RELATED STRUCTURES IN AMALGAMATED DUPLICATION RINGS ⋮ Comaximal graph of amalgamated algebras along an ideal

Cites Work

• Unnamed Item
• A construction of Gorenstein rings
• Coloring of commutative rings
• The zero-divisor graph of a commutative ring
• Beck's coloring of a commutative ring
• When a zero-divisor graph is planar or a complete \(r\)-partite graph
• The diameter of a zero divisor graph
• Zero-divisor graphs of idealizations
• CYCLES AND SYMMETRIES OF ZERO-DIVISORS
• Zero-Divisor Graphs of Polynomials and Power Series Over Commutative Rings
• The Converse to a Theorem of Sharp on Gorenstein Modules

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