Differential operators on monomial rings (Q1295707)

A similar question as in the paper reviewed above [\textit{A. Eriksson}, Commun. Algebra 26, No. 12, 4007-4013 (1998; Zbl 0943.13020)] is considered under more general assumptions, especially in the case where \(k\) has positive characteristic. Apart from the main result (loc. cit.), the structure of \(R\) as a \(D(R)\)-module is described and used in connection with Nakai's conjecture [\textit{B. Singh}, Nagoya Math. J. 103, 67-84 (1986; Zbl 0569.13003)] and determination of the test ideal for tight closure [\textit{C. Huneke}, ``Tight closure and its applications'', Regional Conf. Ser. Math. 88 (1996; Zbl 0930.13004)].