[Preliminary Version] UNIFORM TEST EXPONENTS FOR RINGS OF FINITE F-REPRESENTATION TYPE
نویسنده
چکیده
Let R be a commutative Noetherian ring of prime characteristic p. Assume R (or, more generally, a finitely generated R-module N with SuppR(N) = Spec(R)) has finite F-representation type (abbreviated FFRT) by finitely generated R-modules. Then, for every c ∈ R◦, there is a uniform test exponent Q = p for c and for all R-modules. As a consequence, we show the existence of uniform test exponents over binomial rings (in particular, affine semi-group rings). The existence of uniform test exponents (for all modules) implies that the tight closure coincides with the finitistic tight closure, and tight closure commutes with localization for all R-modules.
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