We abstract the notion of fraction-density of f-rings (introduced by Anthony Hager and Jorge Martínez) to algebraic frames. We say an algebraic frame with the finite intersection property on compact elements is fraction-dense if each of its polars is a polar of a compact element. This turns out to be a “conservative” extension of the fraction-density property in the sense that a reduced f-ring is fraction-dense precisely when its frame of radical ideals is fraction-dense. We characterize these frames and study properties of some other types of algebraic frames that arise naturally in the characterizations of the fraction-dense ones.

中文翻译：

---

在分数密集代数框架上

我们将f环的分数密度的概念（由 Anthony Hager 和 Jorge Martínez 引入）抽象为代数框架。我们说一个在紧元上具有有限相交性质的代数框架是分数密集的，如果它的每一个极点都是紧元的一个极点。这被证明是分数密度属性的“保守”扩展，因为当它的激进理想框架是分数密集时，简化的f环恰好是分数密集的。我们对这些框架进行了表征，并研究了在分数密集框架的表征中自然出现的一些其他类型的代数框架的特性。