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Shows finiteness properties of D-modules in graded rings, indicating significant constraints on module generation and primes.
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.
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Takagi et al. (2008) studied this question.
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