Zero divisor graph of a lattice with respect to an ideal

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• 作者：Mojgan Afkhami (1)
  Kazem Khashyarmanesh (2)
  Khosro Nafar (2)
  
  1. Department of Mathematics ; University of Neyshabur ; P.O. Box 91136-899 ; Neyshabur ; Iran
  2. Department of Pure Mathematics ; Ferdowsi University of Mashhad ; P.O. Box 1159鈥?1775 ; Mashhad ; Iran
  
• 关键词：Zero ; divisor graph ; Lattice ; Clique number ; Chromatic number ; 05C99 ; 06B99
• 刊名：Beitr?ge zur Algebra und Geometrie / Contributions to Algebra and Geometry
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：56
• 期：1
• 页码：217-225
• 全文大小：191 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Algebra
  Convex and Discrete Geometry
  Geometry
  Algebraic Geometry
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：2191-0383

文摘

In this paper, for a bounded lattice \(L\) and an ideal \(I\) of \(L\) , we introduce the zero-divisor graph of \(L\) with respect to \(I\) , denoted by \(\Gamma _I(L)\) . We study the interplay of lattice-theoretic properties of \(L\) with graph-theoretic properties of \(\Gamma _I(L)\) .