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What is Annihilator Ideal Graph in Lattice Theory about?

The article discusses the annihilator ideal graph of a lattice, denoted as AnnIG(L), which is constructed from the ideals of a lattice with nontrivial annihilators. It establishes that for any atomic lattice, AnnIG(L) is a complete multipartite graph and characterizes lattices whose annihilator ideal graph is planar or complete. The authors also explore various properties of AnnIG(L), including its diameter, girth, and connections to zero-divisor graphs.

Author

Oliver Wekesa

Language

EN