Joint reductions, tight closure, and the Briançon-Skoda theorem. II (Q1340442)

[For part I of this paper see ibid. 147, No. 1, 128-136 (1992; Zbl 0755.13003).] By ``Briançon-Skoda theorem'', one means any result of the type \(\overline {I^ n} \subseteq (I^{n-k})^ \#\), where \(I\) is an ideal, \(n>k\) are integers, and where \(\#\) stands for any operator on ideals (such as identity, tight closure or plus closure). In this paper, which is a sequel to part I (loc. cit.), the author proves versions of the Briançon-Skoda theorem for \(F\)-rational rings, for regular rings, for plus closure and some versions with ``multipliers''.