Fregularity
Fregularity is a property studied in commutative algebra and algebraic geometry, defined for Noetherian rings (often local rings) of prime characteristic p > 0. It sits in the framework of tight closure theory and Frobenius endomorphisms, providing a way to measure how mild a ring’s singularities are in positive characteristic. In many texts the terms “strongly F-regular” and “F-regular” are used, with the former emphasizing a stronger technical condition; in practice they are closely related and often taken to coincide.
A common formulation is that a Noetherian ring R of characteristic p > 0 is strongly F-regular if,
Key consequences of F-regularity include favorable singularity properties: strongly F-regular rings are typically Cohen–Macaulay and normal,
Examples and scope: all regular rings of characteristic p are strongly F-regular, and a wide class of