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Details for article 16 of 25 found articles
| Title: |
On the Zero-Divisor Graph of a Ring |
| Author: |
Anderson, David F. Badawi, Ayman |
| Appeared in: |
Communications in algebra |
| Paging: | Volume 36 (2008) nr. 8 pages 3073-3092 |
| Year: |
2008-08 |
| Contents: |
Let R be a commutative ring with identity, Z(R) its set of zero-divisors, and Nil(R) its ideal of nilpotent elements. The zero-divisor graph of R is Γ(R) = Z(R)\{0}, with distinct vertices x and y adjacent if and only if xy = 0. In this article, we study Γ(R) for rings R with nonzero zero-divisors which satisfy certain divisibility conditions between elements of R or comparability conditions between ideals or prime ideals of R. These rings include chained rings, rings R whose prime ideals contained in Z(R) are linearly ordered, and rings R such that {0} ≠ Nil(R) ⊆ zR for all z ∈ Z(R)\Nil(R). |
| Publisher: |
Taylor & Francis |
| Source file: |
Elektronische Wetenschappelijke Tijdschriften |
Details for article 16 of 25 found articles
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