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

Hamid Reza Maimani; Siamak Yassemi

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

Combinatorics 2007-05-23 v1

Authors: Hamid Reza Maimani , Siamak Yassemi

Abstract

Let $R$ be a commutative ring with identity and let $I$ be an ideal of $R$ . Let $R\Join I$ be the subring of $R\times R$ consisting of the elements $(r,r+i)$ for $r\in R$ and $i\in I$ . We study the diameter and girth of the zero-divisor graph of the ring $R\Join I$ .

Keywords

zero-divisor graph amalgamated duplication commutative ring ideal diameter girth

Cite

@article{arxiv.math/0701631,
  title  = {Zero-divisor graphs of amalgamated duplication of a ring along an ideal},
  author = {Hamid Reza Maimani and Siamak Yassemi},
  journal= {arXiv preprint arXiv:math/0701631},
  year   = {2007}
}

Comments

9 pages

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