✦ LIBER ✦

The Zero-Divisor Graph of a Lattice

✍ Scribed by E. Estaji; K. Khashyarmanesh

Publisher: Springer
Year: 2010
Tongue: English
Weight: 179 KB
Volume: 61
Category: Article
ISSN: 1422-6383
DOI: 10.1007/s00025-010-0067-8

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

The Zero-Divisor Graph of a Commutative

The Zero-Divisor Graph of a Commutative Ring

✍ David F. Anderson; Philip S. Livingston 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 121 KB

For each commutative ring R we associate a simple graph ⌫ R . We investigate the interplay between the ring-theoretic properties of R and the graph-theo-Ž . retic properties of ⌫ R .

The zero-divisor graph of a commutative

The zero-divisor graph of a commutative semigroup

✍ F. R. DeMeyer; T. McKenzie; K. Schneider 📂 Article 📅 2002 🏛 Springer 🌐 English ⚖ 109 KB

On the zero-divisor graph of a commutati

On the zero-divisor graph of a commutative ring

✍ S. Akbari; A. Mohammadian 📂 Article 📅 2004 🏛 Elsevier Science 🌐 English ⚖ 192 KB

Let R be a commutative ring and Γ (R) be its zero-divisor graph. In this paper it is shown that for any finite commutative ring R, the edge chromatic number of Γ (R) is equal to the maximum degree of Γ (R), unless Γ (R) is a complete graph of odd order. In [D.F.

When a zero-divisor graph is planar or a

When a zero-divisor graph is planar or a complete r-partite graph

✍ S. Akbari; H.R. Maimani; S. Yassemi 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 218 KB

Let Γ (R) be the zero-divisor graph of a commutative ring R. An interesting question was proposed by Anderson, Frazier, Lauve, and Livingston: For which finite commutative rings R is Γ (R) planar? We give an answer to this question. More precisely, we prove that if R is a local ring with at least 3

Commutative rings whose zero-divisor gra

Commutative rings whose zero-divisor graph is a proper refinement of a star graph

✍ Qiong Liu; Tong Suo Wu 📂 Article 📅 2011 🏛 Institute of Mathematics, Chinese Academy of Scien 🌐 English ⚖ 256 KB

Zero-divisor graphs of partially ordered

Zero-divisor graphs of partially ordered sets

✍ Zhanjun Xue; Sanyang Liu 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 448 KB

Let (P, ≤) be a partially ordered set (poset, briefly) with a least element 0 and S ⊆ P. An element x ∈ P is a lower bound of S if s ≥ x for all s ∈ S. A simple graph G(P) is associated to each poset P with 0. The vertices of the graph are labeled by the elements of P, and two vertices x, y are conn