We consider ordered universal algebras and give a construction of a join-completion for them using so-called \(\mathscr {D}\)-ideals. We show that this construction has a universal property that induces a reflector from a certain category of ordered algebras to the category of sup-algebras. Our results generalize several earlier known results about different ordered structures.

中文翻译：

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有序代数的可接受子集和补全

我们考虑有序的通用代数，并使用所谓的\(\mathscr {D}\) -ideals 为它们提供连接完成的构造。我们表明，该构造具有普遍属性，可将反射器从有序代数的特定类别引入超代数类别。我们的结果概括了关于不同有序结构的几个早期已知结果。