演化代数中的连通理想及其关联图的遗传子集
Connecting ideals in evolution algebras with hereditary subsets of its associated graph
摘要：
本文引入了演化代数的理想与其关联图的顶点遗传子集之间的关系，并建立了它们之间的一些性质。这个关系使我们能够确定极大理想和理想的吸收性质的发展代数在其相关的图。我们还定义了两个保序映射，一个是从进化代数的理想集到对应图的遗传子集的理想集，另一个是从对应图的遗传子集到进化代数的理想集的保序映射。方便地限制在吸收理想集和遗传饱和子集集，这是一个单调伽罗瓦连接。根据该图，我们刻画了任意维有限生成（作为代数）演化代数在其图的某些限制下的特征。在此基础上，给出了有限生成完美发展代数的简单性刻画。
英文摘要：
In this article, we introduce a relation including ideals of an evolution algebra and hereditary subsets of vertices of its associated graph and establish some properties among them. This relation allows us to determine maximal ideals and ideals having the absorption property of an evolution algebra in terms of its associated graph. We also define a couple of order-preserving maps, one from the sets of ideals of an evolution algebra to that of hereditary subsets of the corresponding graph, and the other in the reverse direction. Conveniently restricted to the set of absorption ideals and to the set of hereditary saturated subsets, this is a monotone Galois connection. According to the graph, we characterize arbitrary dimensional finitely-generated (as algebras) evolution algebras under certain restrictions of its graph. Furthermore, the simplicity of finitely-generated perfect evolution algebras is described on the basis of the simplicity of the graph.
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