In this paper, we focus on the structure of the variety of Lie algebras with a finite number of ideals and their graph representations using Hasse diagrams. The large number of necessary conditions on the algebraic structure of this type of algebras leads to the explicit description of those algebras in the variety with trivial Frattini subalgebra. To illustrate our results, we have included and discussed lots of examples throughout the paper.

中文翻译：

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具有有限个理想的李代数

在本文中，我们关注于具有有限个理想的李代数的各种结构及其使用Hasse图的图表示。这种代数的代数结构上的大量必要条件导致对这些具有琐碎的Frattini次代数的代数的明确描述。为了说明我们的结果，我们在本文中包含并讨论了许多示例。