论文标题
混合晶格矢量空间中的理想，频段和直接总和分解
Ideals, bands and direct sum decompositions in mixed lattice vector spaces
论文作者
论文摘要
混合晶格矢量空间是一个部分有序的矢量空间，具有两个部分订购和某些晶格型特性。在本文中，我们首先在混合晶格组中给出了一些基本结果，然后我们研究了混合晶格矢量空间的结构理论，可以将其视为Riesz空间理论的概括。更具体地说，我们研究了混合晶格空间中理想和频段的特性，以及将混合晶格空间表示为直接分离带的相关想法。在某些条件下，这些分解也可以根据订单预测给出。
A mixed lattice vector space is a partially ordered vector space with two partial orderings and certain lattice-type properties. In this paper we first give some fundamental results in mixed lattice groups, and then we investigate the structure theory of mixed lattice vector spaces, which can be viewed as a generalization of the theory of Riesz spaces. More specifically, we study the properties of ideals and bands in mixed lattice spaces, and the related idea of representing a mixed lattice space as a direct sum of disjoint bands. Under certain conditions, these decompositions can also be given in terms of order projections.
