Properties of preordered monoids are investigated and important subclasses of such structures are studied. The corresponding full subcategories are related between them by appropriate functors as well as with the categories of preordered sets and of monoids. Schreier split extensions are described in the full subcategory of preordered monoids whose preorder is determined by the corresponding positive cone.

中文翻译：

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Schreier拆分的预分体的扩展

研究了预排序的mono半群的性质，并研究了此类结构的重要子类。相应的完整子类别之间通过适当的函子以及预排序集和monoid的类别进行关联。Schreier分裂扩展在预排序的类半群的完整子类别中进行了描述，其预排序由相应的正圆锥确定。