In [Schwede 2010], uniformly $F$-compatible ideals were introduced as a generalization of centers of $F$-purity in prime characteristic, revealing deep connections to classical Matlis duality. When the underlying ring is Gorenstein, this notion coincides with the well-studied $F$-ideals of [Smith 1995] and [Kimura 2025]. In this talk, we will introduce the definition and core properties of uniformly $F$-compatible ideals. We will then present our recent result showing that uniformly $F$-compatible ideals cannot be generated by a regular sequence, refining known statements for $F$-ideals.