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

By H. Maimani, Siamak Yassemi. 2007

59 citations recorded by the source corpus.

Abstract Let R be a commutative ring with identity and let I be an ideal of R . Let R ⋈ I be the subring of R × R consisting of the elements ( r , r + i ) for r ∈ R and i ∈ I . We study the diameter and girth of the zero-divisor graph of the ring R ⋈ I .

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/5696fcae359cfaabece107b81d9aeb64e6c91387

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In Algebra and Number Theory

1. Marco Fontana
2. Marco D'anna
3. C. Finocchiaro

In Geometry and Topology

1. Marco Fontana
2. Marco D'anna
3. C. Finocchiaro

Citations in the corpus

• The amalgamated duplication of a ring along a multiplicative-canonical ideal (2006, background): “Note also that this new construction has already been applied for studying questions concerning the diameter and girth of the zero-divisor graph of a ring (see [12]).”
• New Algebraic Properties of an Amalgamated Algebra Along an Ideal (2016, unknown): “, for instance, [4], [5], [8], [12], [13], [20], and [25]).”