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The aim of this paper is to introduce a new class of Noetherian rings ofpositive characteristic in terms of perfect closures and study their basicproperties. If the perfect closure of a Noetherian ring is coherent, we call itan $F$-coherent ring. Some interesting applications are given in connectionwith tight closure theory. In particular, we discuss relationships between$F$-coherent rings and $F$-pure, $F$-regular, and $F$-injective rings. Thefinal section discusses how the coherent property effects the behavior of tightclosure for general perfect rings.

F-coherent rings with applications to tight closure theory