Tight Closure in Non–equidimensional Rings
نویسنده
چکیده
Throughout our discussion, all rings are commutative, Noetherian and have an identity element. The notion of the tight closure of an ideal was developed by M. Hochster and C. Huneke in [HH1] and has yielded many elegant and powerful results in commutative algebra. The theory leads to the notion of F–rational rings, defined by R. Fedder and K.-i. Watanabe as rings in which parameter ideals are tightly closed, see [FW]. Over a field of characteristic zero, rings of F–rational type are now known to be precisely those having rational singularities by the work of K. E. Smith and N. Hara, see [Sm, Ha].
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