introduced the notion of finite F-representation type as a characteristic p analogue of the notion of finite representation type. In this paper, we prove two finiteness properties of rings with finite F-representation type. The first property states that if R = L n0 Rn is a Noetherian graded ring with finite (graded) F-representation type, then for every non-zerodivisor x R, Rx is generated by 1/x as a D R -module. The second one states that if R is a Gorenstein ring with finite F-representation type, then H n I (R) has only finitely many associated primes for any ideal I of R and any integer n. We also include a result on the discreteness of F-jumping exponents of ideals of rings with finite (graded) F-representation type as an appendix.
Takagi et al. (Tue,) studied this question.