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The annihilating-ideal graph of a lattice
-
Mojgan Afkhami
,
Solmaz Bahrami
Published/Copyright:
July 31, 2015
Abstract
Let L = (L,∧,∨) be a lattice with a least element called zero and denoted by 0. The annihilating-ideal graph of L, denoted by 𝔸𝔾(L), is a graph whose vertex-set is the set of all non-trivial ideals of L and, for every two distinct vertices I and J, I is adjacent to J if and only if I ∧ J = {0}. In this paper, we study some properties of 𝔸𝔾(L). Also, we completely determine when the annihilating-ideal graph is complete bipartite, split and end-regular.
The authors would like to thank the referee for the careful reading of the manuscript and the helpful comments.
Received: 2013-12-18
Revised: 2014-7-6
Accepted: 2014-7-8
Published Online: 2015-7-31
Published in Print: 2016-3-1
© 2016 by De Gruyter
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Articles in the same Issue
- Frontmatter
- The annihilating-ideal graph of a lattice
- On derivations and commutativity of prime rings with involution
- On the traces of certain classes of permuting mappings in rings
- Measurability properties of certain paradoxical subsets of the real line
- Some classical Tauberian theorems for (C,1,1,1) summable triple sequences
- Approximation by trigonometric polynomials in the framework of variable exponent grand Lebesgue spaces
- Irrationality measures for almost periodic continued fractions
- Elementary volume and measurability properties of additive functions
- On (n+1)-Hom-Lie algebras induced by n-Hom-Lie algebras
- Generalization of Hermite–Hadamard type inequalities for n-times differentiable functions through preinvexity
- Nonlinear iterative algorithms for quasi contraction mapping in modular space
- n-dimensional quintic and sextic functional equations and their stabilities in Felbin type spaces
- Some remarks on quasi-Frobenius rings
