SOME CONDITIONS FOR THE EQUIVALENCE OF WEAK AND STRONG F-REGULARITY

ABSTRACT

We show that all forms of F-regularity are equivalent for rings in which a sufficiently large symbolic power of an anti-canonical ideal has small enough analytic spread. We also show that if R is weakly F-regular and has a two-generated anti-canonical ideal then R is strongly F-regular. Both of these results then have implications for the existence of test elements.