[HTML][HTML] Zero-divisor graphs of amalgamated duplication of a ring along an ideal
HR Maimani, S Yassemi - Journal of Pure and Applied Algebra, 2008 - Elsevier
Journal of Pure and Applied Algebra, 2008•Elsevier
… We study the diameter and girth of the zero-divisor graph of the ring R ⋈ I . … [7], where it
was known for a trivial extension (more precisely, if R is a Cohen–Macaulay local ring, then
R ( + ) I is Gorenstein if and only if I is a canonical ideal); cf. [13]. This was our motivation for
studying the zero-divisor graph of R ⋈ I . …
was known for a trivial extension (more precisely, if R is a Cohen–Macaulay local ring, then
R ( + ) I is Gorenstein if and only if I is a canonical ideal); cf. [13]. This was our motivation for
studying the zero-divisor graph of R ⋈ I . …
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.
Elsevier
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